Nestor Partners 10-Q 2010 Q2 Quarterly report

Exhibit 32.03

CERTIFICATION PURSUANT TO SECTION 1350 OF CHAPTER 63 OF TITLE 18 OF

THE UNITED STATES CODE

I,    Gregg Buckbinder, certify that (i) the Quarterly Report of Nestor Partners (the “Partnership”) on Form 10-Q for the period ending June 30, 2010 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

Millburn Ridgefield Corporation

General Partner, Nestor Partners

August 13, 2010