"Tribute to the Music of Bob Wills and the Texas Playboys" earned Asleep at the Wheel its 12th, 13th and 14th Grammy Award nominations, and its fourth and fifth wins. At the 36th Annual Grammy Awards in 1994, opening track and lead single "Red Wing" won the Grammy Award for Best Country Instrumental Performance, the band's fourth win in the category. At the 37th Annual Grammy Awards the next year, "Blues for Dixie" won the Grammy Award for Best Country Performance by a Duo or Group with Vocal, while the album received a nomination for Best Country Album. The album was nominated for Album of the Year at the 1994 Country Music Association Awards, losing out to another tribute album, "".