Graves has received many awards, including the Grand Prix du Concours International de Chant de Paris, the Eleanor Steber Music Award in the Opera Columbus Vocal Competition, and a Jacobson Study Grant from the Richard Tucker Music Foundation
. In 1991, she received the Grand Prix Lyrique, awarded once every three years by the Association des amis de I'opera de Monte-Carlo, and the Marian Anderson Award.
Minkin was also a trustee of several non-profits, including Long Island University, the Richard Tucker Music Foundation
and the Brooklyn Bureau of Community Service.
Besides the Metropolitan Opera auditions, she also has won a Robert Jacobsen Study Grant from the Richard Tucker Music Foundation
, the Liederkranza Foundation Competition and the Joy in Singing Award.