Diamond Offshore Drilling (DODRW) 10-Q 2012 Q2 Quarterly report

Exhibit 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED BY SECTION 906

OF THE SARBANES-OXLEY ACT OF 2002

Each of the undersigned hereby certifies, pursuant to 18 U.S.C. § 1350, in his capacity as an officer of Diamond Offshore Drilling, Inc. (the “Company”), that, to his knowledge:

(1) the Company’s Quarterly Report on Form 10-Q for the quarter ended June 30, 2012 as filed with the U.S. Securities and Exchange Commission on the date hereof (the “Report”), fully complies with the requirements of Section 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.

Dated: July 26, 2012

/s/ Lawrence R. Dickerson                            

Lawrence R. Dickerson

Chief Executive Officer of the Company

/s/ Gary T. Krenek                                          

Gary T. Krenek

Chief Financial Officer of the Company