Kunkel officiated in the World Series in 1974 and 1980, and in the American League Championship Series in 1971, 1975, 1978 and 1982. He also worked the All-Star Game in 1972 and 1977, calling balls and strikes for the second contest. Kunkel's experience as the plate umpire is documented in the MLB official highlight film of the 1977 All-Star Game.