Montague was born in San Francisco, California. He umpired the World Series in 1986, 1991, 1997, 2000, 2004 and 2007, serving as crew chief on the last four occasions; only Bill Klem (9 times) and Bill Summers (4 times) held the position of World Series crew chief as often. Montague also umpired in the All-Star Game in 1982, 1990, 1998 and 2004, calling balls and strikes for the last three contests. He is only the fourth umpire in history—joining Bill McGowan, Summers and Al Barlick—to serve as crew chief for three World Series and as home plate umpire for three All-Star Games. In 2004, he became the first umpire to work behind the plate for the entire All-Star Game and serve as crew chief in the World Series in the same season.