ResMed (RMD) 10-K 2024 FY Annual report

EXHIBIT 32.1

The following certifications are being furnished solely to accompany the Annual Report pursuant to 18 U.S.C. Section 1350 and in accordance with SEC Release No. 33-8238. These certifications shall not be deemed “filed” for purposes of Section 18 of the Securities Exchange Act of 1934, as amended, nor shall they be incorporated by reference in any filing made by ResMed Inc. under the Securities Act of 1933, as amended, whether made before or after the date hereof, regardless of any general incorporation language in such filing.

CERTIFICATIONS OF CHIEF EXECUTIVE OFFICER AND CHIEF FINANCIAL OFFICER

PURSUANT TO 18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

Pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, I, Michael J. Farrell, Chief Executive Officer of ResMed Inc., a Delaware corporation (the “Company”), hereby certify that to my knowledge:

(i)the accompanying Annual Report on Form 10-K of the Company for the year ended June 30, 2024 (the “Annual Report”) fully complies with the requirements of Section 13(a) or Section 15(d), as applicable, of the Securities Exchange Act of 1934, as amended; and

(ii)the information contained in the Annual Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

August 8, 2024

/s/ MICHAEL J. FARRELL

Michael J. Farrell

Chief Executive Officer

(Principal Executive Officer)

Pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, I, Brett A. Sandercock, Chief Financial Officer of the Company, hereby certify that to my knowledge:

(i)the accompanying Annual Report fully complies with the requirements of Section 13(a) or Section 15(d), as applicable, of the Securities Exchange Act of 1934, as amended; and

(ii)the information contained in the Annual Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

August 8, 2024

/s/ BRETT A. SANDERCOCK

Brett A. Sandercock

Chief Financial Officer

(Principal Financial Officer)

A signed original of this written statement required by Section 906 has been provided to ResMed Inc. and will be retained by ResMed Inc. and furnished to the Securities and Exchange Commission or its staff upon request.