ABIOMED 10-Q 2009 Exhibit 32.1 CERTIFICATION PURSUANT TO 18 U.S.C. § 1350 AS ADOPTED PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002 In connection with the Quarterly Report on Form 10-Q of ABIOMED, Inc., (the Company) for the quarter ended December 31, 2008, as filed with the Securities and Exchange Commission on the date hereof (the Report), each of the undersigned President and Chief Executive Officer, and Corporate Controller, of the Company, certifies, to the best knowledge and belief of the signatory, pursuant to 18 U.S.C. § 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 that:
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