EXHIBIT 32.1

CERTIFICATION PURSUANT TO 18 U.S.C. 1350

(SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002)

I, Rhett Bennett, Chief Executive Officer of Black Mountain Acquisition Corp. (the “Company”), certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to my knowledge:

(1) the Quarterly Report on Form 10-Q of the Company for the quarterly period ended March 31, 2023 (the “Report”) fully complies with the requirements of Sections 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

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

This certificate is being furnished solely for the purposes of 18 U.S.C. Section 1350 and is not being filed as part of the Report or as a separate disclosure document.

Date: May 18, 2023

/s/ Rhett Bennett

Rhett Bennett

Chief Executive Officer

(Principal Executive Officer)