Ocean Rig UDW POS AM Prospectus update (post-effective amendment)

Exhibit 5.1

Our ref                 SEA/713299-000001/42036063v3

To the Addressees named in the Schedule

6 July 2016

Dear Sirs

Ocean Rig UDW Inc. – Transfer By Way of Continuation to the Cayman Islands

We are acting as counsel as to Cayman Islands law to Ocean Rig UDW Inc. (the “Company”), a Cayman Islands exempt limited company, registered by way of continuation in the Cayman islands (“Transfer by Way of Continuation”) pursuant to Section 201 of the Companies Law (2013 Revision) of the Cayman Islands (the “Companies Law”), prior to such Transfer by Way of Continuation, the Company was incorporated and existing under the laws of the Republic of the Marshall Islands.

We refer in particular to the 82,586,851 common shares with nominal value of US$0.01 of the Company (the “Common Shares”), the 8,000,000 series A participating preferred shares with nominal value of US$0.01 of the Company (the “Preferred Stock”) and the associated preferred stock purchase rights (the “Preferred Stock Purchase Rights”) of the Company, pursuant to a post-effective amendment no. 1 to Form F-4 Registration Statement (“Registration Statement”) which has been filed on the date hereof with the United States Securities and Exchange Commission (the “SEC”) under the Securities Act of 1933.

1 Documents Reviewed

We have reviewed originals, copies, drafts or conformed copies of the following documents:

1.1 The certificate of registration by way of continuation dated 14 April 2016 (“Certificate of Registration”) and the second amended and restated articles of incorporation of the Company as filed on 3 May 2011 with the Registrar of Corporations of the Republic of the Marshall Islands (the “Articles”) and the second amended and restated bylaws of the Company as adopted on 9 March 2011 (the “Bylaws”).

1.2 The written resolutions of the board of directors of the Company dated 27 April 2016 (the “Resolutions”);

1.3 A certificate of good standing with respect to the Company issued by the Registrar of Companies dated 6 July 2016 (the “Certificate of Good Standing”).

1.4 the Registration Statement; and

1.5 Such other documents as we have considered necessary for the purpose of rendering this opinion.

2 Assumptions

The following opinions are given only as to, and based on, circumstances and matters of fact existing and known to us on the date of this opinion letter. These opinions only relate to the laws of the Cayman Islands which are in force on the date of this opinion letter. In giving the following opinions, we have relied (without further verification) upon the completeness and accuracy of the Certificate of Registration and the Certificate of Good Standing. We have also relied upon the following assumptions, which we have not independently verified:

2.1 Copies of documents, conformed copies or drafts of documents provided to us are true and complete copies of, or in the final forms of, the originals, and translations of documents provided to us are complete and accurate.

2.2 All signatures, initials and seals are genuine.

2.3 Under the laws of the Republic of the Marshall Islands (the “De-Registration Jurisdiction”) and all other relevant laws (other than the laws of the Cayman Islands), at all times relevant for purposes of rendering the opinions as expressed herein, the Company was duly incorporated, validly existing and in good standing under the laws of the De-Registration Jurisdiction and at all times relevant for purposes of rendering our opinions as expressed herein had, the full power, authority and legal right to de-register as a body corporate limited by shares from the De-Registration Jurisdiction and to register by way of continuation as an exempted company limited by shares in the Cayman Islands.

2.4 At all times relevant times for purposes of rendering our opinions as set forth herein, the laws of the De-Registration Jurisdiction permitted the Company to transfer by way of continuation in to the Cayman Islands.

2.5 That the Transfer by Way of Continuation of the Company in to the Cayman Islands pursuant to Section 201 of the Companies Law was by duly authorised by the Company.

2.6 That all necessary action was taken under the applicable laws of the De-Registration Jurisdiction to authorise and permit the Company to Transfer by Way of Continuation in to the Cayman Islands pursuant to Section 201 of the Companies Law and any and all consents, approvals and authorisations from applicable Marshall Islands governmental authorities required to authorise and permit the Company to Transfer by Way of Continuation have been obtained.

2.7 Immediately prior to the Transfer by Way of Continuation, the Common Shares have been, duly and validly authorised, legally and validly issued and fully paid and non-assessable under the laws of the De-Registration Jurisdiction.

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2.8 Immediately prior to the Transfer by Way of Continuation, the Preferred Stock has been, duly and validly authorised under the laws of the De-Registration Jurisdiction.

2.9 Immediately prior to the Transfer by Way of Continuation, the Preferred Stock Purchase Rights and any agreement constituting such rights have been, duly and validly authorised and will be, or are, legal, valid, binding and enforceable under the laws of the De-Registration Jurisdiction and all other laws (other than the laws of the Cayman Islands).

2.10 There is nothing under any law (other than the laws of the Cayman Islands) which would or might affect the opinions set out below. Specifically, we have made no independent investigation of the laws of the De-Registration Jurisdiction and have assumed that the laws of the De-Registration Jurisdiction authorise the Company to continue into the Cayman Islands and that the Company has, or shall, comply fully with the laws of the De-Registration Jurisdiction in respect of the continuation into the Cayman Islands.

2.11 All appropriate entries have been made in the register of members of the Company in respect of the Common Shares.

3 Opinions

Based upon, and subject to, the foregoing assumptions, and having regard to such legal considerations as we deem relevant, we are of the opinion that:

3.1 Upon the issuance of the Certificate of Registration the Company was duly registered by way of continuation as an exempted company under the laws of the Cayman Islands.

3.2 Upon the issuance of the Certificate of Registration, the Common Shares, the Preferred Stock and the associated Preferred Stock Purchase Rights have, by operation of law, been duly and validly authorised, and the Common Shares have been legally and validly issued and fully paid and non-assessable under the laws of the Cayman Islands.

4 Qualifications

This opinion is subject to the following qualification and limitation that under the Companies Law, the register of members of a Cayman Islands company is by statute regarded asprima facie evidence of any matters which the Companies Law directs or authorises to be inserted therein. A third party interest in the shares in question would not appear. An entry in the register of members may yield to a court order for rectification (for example, in the event of fraud or manifest error).

Except as specifically stated herein, we make no comment with respect to any representations and warranties which may be made by or with respect to the Company in any of the documents or instruments cited in this opinion or otherwise with respect to the commercial terms of the transactions the subject of this opinion.

We express no view as to the commercial terms of the de-registration in the De-Registration Jurisdiction or the registration by way of continuation in the Cayman Islands. The opinions in this opinion letter are strictly limited to the matters contained in the opinions section above and do not extend to any other matters.

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This opinion is issued solely for the purpose of filing of the Registration Statement and the registration of the Common Shares and the Preferred Stock Rights by the Company and is strictly limited to the matters stated herein and is not to be relied upon in respect of any other matter.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement, and to the reference to us under the heading “Legal Matters” in the Prospectus, without admitting we are “experts” within the meaning of the Securities Act of 1933, as amended, or the rules and regulations of the SEC thereunder with respect to any part of the Registration Statement.

Yours faithfully

/s/ Maples and Calder

Maples and Calder

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Schedule

List of Addressees

Ocean Rig UDW Inc.

10 Skopa Street, Tribune House

2nd Floor, Office 202, CY 1075

Nicosia, Cyprus