Capital Clean Energy Carriers (CCEC) F-3 Shelf registration (foreign)

Exhibit 5.1

Capital Clean Energy Carriers Corp.

3, Iassonos Street

Piraeus, Athens

18537, Greece

Our reference: 24435.50035/80917227v2

October 11, 2024

Registration Statement on Form F-3: Exhibit 5.1

Dear Sirs:

We have acted as special counsel as to matters of the law of the Republic of the Marshall Islands (“Marshall Islands Law”) for Capital Clean Energy Carriers Corp., a Marshall Islands corporation (the “Corporation”), in connection with the preparation and filing with the Securities and Exchange Commission (the “Commission”), pursuant to the Securities Act of 1933, as amended (the “Securities Act”), and the rules and regulations promulgated thereunder (“Rules”), of a registration statement on Form F-3 (such registration statement and any additional registration statement filed pursuant to Rule 462(b) is referred to as the “Registration Statement”) for the registration of the sale from time to time by the Corporation of an aggregate of $500,000,000 of the Corporation’s securities, consisting of:

a) the Corporation’s common shares, par value $0.01 per share (“Common Shares”);

b) the Corporation’s preferred stock, par value $0.01 per share (“Preferred Shares”), which may be convertible into other securities of the Corporation;

c) debt securities of the Corporation (“Debt Securities”) including convertible debt securities, which may be issued pursuant to a form of indenture for debt securities in the form filed as Exhibit 4.3 to the Registration Statement (the “Indenture”); and

d) rights to purchase the Corporation’s securities (“Rights” and collectively with the Common Shares, Preferred Shares and Debt Securities, the “Securities”).

The Securities will be sold from time to time as set forth in the Registration Statement, the prospectus contained therein (the “Prospectus”) and supplements to the Prospectus (the “Prospectus Supplements”).

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In rendering this opinion, we have examined originals or photocopies of all such documents, including:

(i) the Registration Statement and the Prospectus;

(ii) the Indenture;

(iii) the Corporation’s Bylaws (the “Bylaws”) and Articles of Incorporation dated as of August 26, 2024 (the “Articles” and together with the Bylaws, the “Organizational Documents”); and

(iv) such other papers, documents, agreements, and certificates of public officials and certificates of officers or representatives of the Corporation, as we have deemed relevant or necessary as the basis for the opinions hereafter expressed.

In such examination, we have assumed: (a) the legal competence or capacity of each natural person or entity (other than the Corporation), (b) the genuineness of all signatures, including electronic signatures, and the authenticity of all documents submitted to us as originals, (c) the conformity to original documents of all documents submitted to us as conformed or photostatic copies, (d) that the documents reviewed by us in connection with the rendering of the opinions set forth herein are true, correct and complete, and (e) the truthfulness of each statement as to all factual matters contained in any document or certificate encompassed within the due diligence review undertaken by us. We have also assumed the power, authority and legal right of all parties (other than the Corporation) to the Registration Statement and any amendments or supplements thereto (including any necessary post-effective amendments), and all parties to the Indenture (other than the Corporation), to enter into and perform their respective obligations thereunder, and the due authorization, execution and delivery of the Indenture by all parties thereto. We have further assumed the validity and enforceability of all documents under all applicable laws other than Marshall Islands Law. As to any questions of fact material to our opinion that have not been independently established, we have relied upon the representations and certificates of officers or representatives of the Corporation and of public officials, in each case as we have deemed relevant or appropriate. We have not independently verified the facts so relied on.

We have also assumed that (i) the Registration Statement and any amendments or supplements thereto (including any necessary post-effective amendments) shall have become effective under the Securities Act, (ii) a Prospectus Supplement or, as applicable, term sheet, shall have been prepared and filed with the Commission describing the Securities offered thereby, (iii) the Securities shall be issued and sold in compliance with applicable U.S. federal, state and foreign laws and in the manner stated in the Registration Statement and the applicable Prospectus Supplement or term sheet, and not more than the maximum dollar value of Securities will be sold than the maximum dollar amount set forth in the Registration Statement, (iv) a definitive purchase agreement, underwriting agreement or similar agreement with respect to any Securities offered will have been duly authorized and validly executed and delivered by the applicable registrants and the other parties thereto, (v) any Securities, including Securities issuable upon conversion, exchange or exercise of any Security being offered, will be duly authorized, created and, if appropriate, reserved for issuance upon such conversion, exchange or exercise, and will be validly issued, and the certificates, if any, evidencing the same will be duly executed and delivered, against receipt of the consideration approved by the Corporation, (vi) each Common Share and Preferred Share will be sold or issued (including if issued upon conversion or exchange of another Security) at a price not less than the par value thereof, (vii) the definitive terms of any Security, other than Common Shares,

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offered pursuant to the Registration Statement will have been established in accordance with resolutions of the Board of Directors of the Corporation (and shareholders of the Corporation, if applicable), the Organizational Documents and applicable law, (viii) the terms of the offer and sale of Securities and the issuance and, if applicable, sale of and payment for the Securities are duly authorized and complies in all respects with the terms, conditions and restrictions set forth in the Organizational Documents, Registration Statement, Prospectus, Prospectus Supplement and, as applicable, Indenture, and all of the instruments and other documents relating thereto or executed in connection therewith, and (ix) all documents contemplated by the Prospectus, including any supplement or amendment thereto, to be executed in connection with the offer and sale of Securities will have been duly authorized, executed and delivered by each of the parties thereto.

We have assumed that the Corporation will, at the time of any issuance of Common Shares or Preferred Shares, have a sufficient number of authorized but unissued Common Shares or Preferred Shares pursuant to its Articles to so issue (whether directly or upon conversion or exchange of another Security) the relevant number of shares, after taking into account shares reserved for issuance.

With respect to the issuance and sale of any series of Preferred Shares, we have further assumed that an appropriate statement of designations or similar instrument setting forth the preferential, deferred, qualified or special rights, powers, privileges, conditions or duties with respect to such series of Preferred Shares, or an amendment to the Organizational Documents, will have been duly adopted and fixed by the Board of Directors of the Corporation (and the shareholders of the Corporation, as applicable) in a form to be described in a Prospectus Supplement, all in conformity with the requirements of the Organizational Documents and applicable law.

With respect to the issuance and sale of any Debt Securities, we have further assumed that (i) the relevant Indenture will be duly qualified under the Trust Indenture Act of 1939, as amended, with respect to the Trustee executing the applicable Indenture, and a Form T-1 shall have been filed with the U.S. Securities and Exchange Commission and become effective under the Trust Indenture Act of 1939, as amended; (ii) the relevant Indenture will have been duly executed and delivered by the Corporation and the trustee named therein (the “Trustee”) substantially in the form examined by us and any applicable supplemental indenture will have been duly executed and delivered by the Corporation and the Trustee in accordance with the terms and conditions of the relevant Indenture regarding the creation, authentication and delivery of any supplemental indenture to such Indenture and (iii) such Debt Securities when issued, will be executed, authenticated, issued and delivered (a) against receipt of the consideration therefor approved by the Corporation and (b) as provided in the relevant Indenture with respect thereto and the other applicable definitive purchase, underwriting, or similar agreement approved by the Corporation and as contemplated in the Prospectus or Prospectus Supplement related thereto, against payment of the consideration therefor as provided for therein.

With respect to the issuance and sale of any Rights, we have further assumed that the respective documents and agreements (“Rights Documents”) relating to the creation, offering, issuance and sale of the Rights will have been duly authorized, executed and delivered and are enforceable in accordance with their terms, that the Rights Documents, as necessary, have been duly executed and countersigned in accordance with the applicable Rights Documents and the Rights will be created, offered, issued and sold as contemplated in the Registration Statement, the applicable authorizing resolutions, the Organizational Documents and the applicable Rights Documents.

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This opinion is limited to Marshall Islands Law and is as of the date hereof. We expressly disclaim any responsibility to advise of any development or circumstance of any kind, including any change of law or fact or the impact of any information, document, certificate, record, statement, representation, covenant, or assumption relied upon herein that becomes incorrect or untrue, that may occur after the date of this opinion letter that might affect the opinion expressed herein.

Based on the foregoing, and having regard to legal considerations which we deem relevant, and subject to the qualifications, limitations and assumptions set forth herein, we are of the opinion that:

1. The Corporation is validly existing under Marshall Islands Law.

2. The Corporation has the corporate power to enter into the Indenture.

3. When the terms of the issuance and sale thereof, the terms of the offering thereof and related matters have been duly authorized and approved by the Corporation, and when issued and delivered by the Corporation against payment therefor in accordance with the terms of the Organizational Documents, the applicable purchase, underwriting or similar agreement and the Registration Statement, Prospectus and a Prospectus Supplement, the Common Shares will be validly issued, fully paid and non-assessable.

4. When the terms of the issuance and sale thereof, the terms of the offering thereof and related matters have been duly authorized and approved by the Corporation, and when issued and delivered by the Corporation against payment therefor in accordance with the terms of the Organizational Documents, the applicable purchase, underwriting or similar agreement and the Registration Statement, Prospectus and Prospectus Supplement, the Preferred Shares will be validly issued, fully paid and non-assessable, and if the Preferred Shares are convertible into Common Shares or other Preferred Shares, then such resulting Common Shares or Preferred Shares upon conversion will be (subject to compliance with the requirements set forth in this Paragraph and Paragraph 3 above), validly issued, fully paid and non-assessable.

5. When the terms of the issuance and sale thereof, the terms of the offering thereof and related matters have been duly authorized and approved by the Corporation, and when issued and delivered against payment therefor in accordance with the terms of the Organizational Documents, the applicable purchase, underwriting or similar agreement, and the Registration Statement, Prospectus and Prospectus Supplement, and after the Corporation has received the consideration for the Rights provided for in the applicable Rights Documents, if the Rights are convertible into Common Shares or Preferred Shares, then such resulting Common Shares or Preferred Shares will be (subject to compliance with the requirements set forth in Paragraphs 3 and 4 above), validly issued, fully paid and non-assessable.

6. Upon the due execution and delivery of the Indenture by the Corporation and the other parties thereto substantially in the form examined by us, when (a) the specific terms of a particular Debt Security have been duly authorized by the Corporation and established in accordance with the Indenture, and (b) such Debt Security has been duly executed, authenticated, issued for value and delivered in accordance with such Indenture, and if the Debt Securities are convertible into Common Shares or Preferred Shares, then such resulting Common Shares or Preferred Shares will be (subject to compliance with the requirements set forth in Paragraphs 3 and 4 above), validly issued, fully paid and non-assessable.

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We consent to the filing of this opinion as an exhibit to the Registration Statement, to the discussion of this opinion in the Registration Statement, and to the references to our firm in the Prospectus. In giving this consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or related Rules, nor do we admit that we are experts with respect to any part of the Registration Statement within the meaning of the term “expert” as used in the Securities Act or related Rules.

Very truly yours,

Watson Farley & Williams LLP

/s/ Watson Farley & Williams LLP