During her career Gravina won a number of international awards, including the Best Actress Award for her performance in Alessandro Blasetti's "Love and Chatter" at the 1958 Locarno International Film Festival, the award for Best Supporting Actress for her role in Ettore Scola's "La terrazza" at the 1980 Cannes Film Festival, and the award for Best Actress for Margarethe von Trotta's "The Long Silence" at the 1993 Montreal World Film Festival.