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), 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 Annual Report on Form 10-K for the year ended December 31, 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:	February 23, 2024	/s/ THOMAS E. JORDEN
		Thomas E. Jorden Chief Executive Officer
		/s/ SHANNON E. YOUNG III
		Shannon E. Young III Chief Financial Officer