EXHIBIT 32.1

Mercury Computer Systems, Inc.

Certification Pursuant To

18 U.S.C. Section 1350,

As Adopted Pursuant To

Section 906 of the Sarbanes-Oxley Act of 2002

In connection with the Quarterly Report of Mercury Computer Systems, Inc. (the “Company”) on Form 10-Q for the period ended March 31, 2005 as filed with the Securities and Exchange Commission (the “Report”), I, James R. Bertelli, President and Chief Executive Officer of the Company, certify, pursuant to Section 1350 of Chapter 63 of Title 18, United States Code, that the Report fully complies with the requirements of Section 13(a) or 15(d), as applicable, of the Securities Exchange Act of 1934, as amended, and that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: May 9, 2005

/s/    JAMES R. BERTELLI        

James R. Bertelli

PRESIDENT AND CHIEF EXECUTIVE OFFICER