Exhibit 32.1

CERTIFICATION PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Annual Report of Apropos Technology, Inc. (the “Company”) on Form 10-Q for the period ending June 30, 2004 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), the undersigned Chief Financial Officer of the Company hereby certify, pursuant to 18 U.S.C. §1350, as adopted pursuant to §906 of the Sarbanes-Oxley Act of 2002 that based on their 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 as of and for the periods covered in the Report.

/s/ Francis J. Leonard

Francis J. Leonard, Chief Financial Officer, Vice President
and Principal Executive Officer

August 13, 2004

A signed original of this written statement required by Section 906, or other document authenticating, acknowledging, or otherwise adopting the signature that appears in typed form within the electronic version of this written statement required by Section 906, has been provided to the Company and will be retained by the Company and furnished to the Securities and Exchange Commission or its staff upon request.

The foregoing certification is being furnished to the Securities and Exchange Commission as an exhibit to the Form 10-Q and shall not be considered filed as part of the Form 10-Q.