Exhibit 32.1 CERTIFICATION OF REGISTRANT'S CHIEF EXECUTIVE OFFICER PURSUANT TO 18 U.S.C. 1350 I, Peter J. Murphy, Chief Executive Officer of Parlex Corporation (the "Company"), do hereby certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to my knowledge: (a) the Quarterly Report on Form 10-Q of the Company for the period ending March 31, 2005, as filed with the Securities and Exchange Commission (the "Report"), fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and (b) the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company. Dated: May 13, 2005 /s/ Peter J. Murphy - ------------------- Peter J. Murphy Chief Executive Officer This certification accompanies this Report on Form 10-Q pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 and shall not, expect to the extent required by such Act, be deemed filed by the Company for purposes of Section 18 of the Securities Exchange Act of 1934, as amended (the "Exchange Act"). Such certification will not be deemed incorporated by reference into any filing under the Securities Act of 1933, as amended, or the Exchange Act, expect to the extent the Company specifically incorporated it by reference.