Exhibit 32.1

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 Millipore Corporation (the “Company”) on Form 10-Q for the period ending June 30, 2003 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), each of the undersigned, Francis J. Lunger, Chief Executive Officer of the Company, and Kathleen B. Allen, Chief Financial Officer of the Company, certifies, pursuant to 18 U.S.C. section 1350, as adopted pursuant to section 906 of the Sarbanes-Oxley Act of 2002, that to his or her knowledge:

(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/    FRANCIS J. LUNGER*         

Francis J. Lunger

President and Chief Executive Officer

August 7, 2003

/s/    KATHLEEN B. ALLEN*         

Kathleen B. Allen

Vice President and Chief Financial Officer

August 7, 2003

*–A signed original of this written statement required by Section 906 has been provided to Millipore Corporation and will be retained by Millipore Corporation and furnished to the Securities and Exchange Commission or its staff upon request.