Melinda was nominated for a Golden Globe in 1977 for Best Acting Debut in a Motion Picture-Female for Bound for Glory.
Melinda has been nominated for two Oscars. In 1977 she was nominated for Best Supporting Role for Close Encounters of the Third Kind. In 1981 she was nominated for Best Supporting Actress for Absense of Malice.
Melinda was nominated for a SAG award in 2000 for Magnolia for Outstanding Performance by a Cast in a Theatrical Motion Picture.