Exhibit 32.1

CERTIFICATION OF CHIEF EXECUTIVE OFFICER AND

CHIEF FINANCIAL OFFICER

Pursuant to 18 U.S.C. § 1350 and in connection with the accompanying report on Form 10-Q for the period ended March 31, 2011 that is being filed concurrently with the Securities and Exchange Commission on the date hereof (the “Report”), each of the undersigned officers of Southwest Royalties Institutional Income Fund X-C, L.P. (the “Company”), hereby certifies that:

1. The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

The information contained in the Report fairly presents, in all material respects, the financial condition and results of operation of the Company.

/s/ Mel G. Riggs

Mel G. Riggs

President and Chief Executive Officer

of Southwest Royalties, Inc., the

Managing General Partner of

Southwest Royalties Institutional Income Fund X-C, L.P.

May 13, 2011

/s/ Michael L. Pollard

Michael L. Pollard

Senior Vice President and Chief Financial Officer

Southwest Royalties, Inc., the

Managing General Partner of

Southwest Royalties Institutional Income Fund X-C, L.P.

May 13, 2011

SOUTHWEST ROYALTIES INSTITUTIONAL INCOME FUND X-C LP 10-Q