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-K for the period ended December 31, 2013 that is being filed concurrently with the Securities and Exchange Commission on the date hereof (the “Report”), each of the undersigned officers of Clayton Williams Energy, Inc. (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

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

/s/ Clayton W. Williams, Jr.

Clayton W. Williams, Jr.

Chief Executive Officer

March 10, 2014

/s/ Michael L. Pollard

Michael L. Pollard

Chief Financial Officer

March 10, 2014