Exhibit 32.1
                                  CERTIFICATION

   Pursuant to 18 U.S.C. 1350 as adopted by Section 906 of the Sarbanes-Oxley
                                  Act of 2002

     In connection with the Quarterly Report of Tiffany & Co. (the "Company") on
Form 10-Q for the period ended April 30, 2005, as filed with the  Securities and
Exchange  Commission on the date hereof (the "Report"),  I, Michael J. Kowalski,
as  Chairman  of the Board of  Directors  and  Chief  Executive  Officer  of the
Company,  certify, pursuant to 18 U.S.C. ss 1350, as adopted pursuant to Section
906 of the Sarbanes-Oxley Act of 2002, 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.


Dated:   June 1, 2005


                                        /s/ Michael J. Kowalski
                                       ____________________________________
                                            Michael J. Kowalski
                                       Chairman and Chief Executive Officer