I think the OP might be referring to The Superintendent's Trophy.
In 2003, the schools jointly established the Superintendent’s Trophy. This contest pits USCGA against USMMA but for the entire academic year. One point is awarded to the winning school after each match, giving all sports equal weight. The school with the highest score is presented with the Superintendent's Trophy in a halftime ceremony at the Secretaries' Cup football game, with the winning school keeping possession of the trophy until the next year.
USCGA has held the Superintendent's Trophy since its inception, USMMA has yet to win it once.