Exhibit 32.1

CERTIFICATION

PURSUANT TO

SECTION 1350 OF CHAPTER 63 OF TITLE 18 OF THE UNITED STATES CODE

I, George Schrade, Principal Financial Officer of Graham Capital Management L.P. and I, Brian Douglas, Principal Executive Officer of Graham Capital Management L.P., certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, 18 U.S.C. Section 1350, that:

1. The Quarterly Report on Form 10-Q of Graham Alternative Investment Fund II LLC Core Macro Portfolio (the “registrant”) for the period ended September 30, 2024 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 registrant.

Date: November 14, 2024

/s/ George Schrade

George Schrade

Principal Financial Officer

Graham Capital Management, L.P.

/s/ Brian Douglas

Brian Douglas

Principal Executive Officer

Graham Capital Management, L.P.