EXHIBIT 32.1 CERTIFICATION OF CHIEF EXECUTIVE OFFICER PURSUANT TO 18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002 I, Moshe BenBassat, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that the Quarterly Report of ClickSoftware Technologies Ltd. on Form 10-Q for the quarter ended March 31, 2004 fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and that information contained in such Quarterly Report on Form 10 Q fairly presents in all material respects the financial condition and results of operations of ClickSoftware Technologies Ltd. as of and for the periods presented in such Report on Form 10-Q. This written statement is being furnished to the Securities and Exchange Commission as an exhibit accompanying such Report and shall not be deemed filed pursuant to the Securities Exchange Act of 1934. Date: May 12, 2004 By: /s/ MOSHE BENBASSAT ------------------------------------------ Name: Moshe BenBassat Title: Chairman and Chief Executive Officer -33-