EXHIBIT 32.1

Certification Pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

(Subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code)

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (Subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code) (the “Act”), each of the undersigned, Thomas E. Jorden, Chief Executive Officer of Coterra Energy Inc., a Delaware corporation (the “Company”), and Shannon E. Young III, Chief Financial Officer of the Company, hereby certify that, to his knowledge:

(1)the Company’s Quarterly Report on Form 10-Q for the quarter ended June 30, 2023 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

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

Dated: August 8, 2023

/s/ THOMAS E. JORDEN

Thomas E. Jorden

Chief Executive Officer

/s/ SHANNON E. YOUNG III

Shannon E. Young III

Chief Financial Officer