Exhibit 32.03 CERTIFICATION PURSUANT TO SECTION 1350 OF CHAPTER 63 OF TITLE 18 OF THE UNITED STATES CODE I, Gregg Buckbinder, the Chief Financial and Operating Officer and principal financial officer of Millburn Ridgefield Corporation, the General Partner of Nestor Partners (the "Partnership"), certify that (i) the Quarterly Report of the Partnership on Form 10-Q for the period ending June 30, 2006 fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and (ii) the information contained in such Quarterly Report fairly presents, in all material respects, the financial condition and results of operations of the Partnership. /s/ Gregg Buckbinder - --------------------------- Gregg Buckbinder Chief Financial and Operating Officer August 14, 2006