He received the James Smithson Medal from the Smithsonian Institution, an American Jazz Masters Award, a National Association of Jazz Educators Hall of Fame Award, a Sagamore of the Wabash award, and a Governor's Arts Award from the State of Indiana. Baker also held leadership positions in several arts and music associations. The Indiana Historical Society named Baker an Indiana Living Legend in 2001. The John F. Kennedy Center for the Performing Arts named him a Living Jazz Legend in 2007.