At the 1908 Olympic Games, Montague won his preliminary heat in the 400 metres with a time of 50.2 seconds. He dropped his time to 49.8 seconds in the semifinals but lost to Wyndam Halswelle, who set a new Olympic record at 48.4 seconds in the race. Montague's second-place finish in the semifinals prevented him from advancing to the final.
He was also a member of the British team, which was eliminated in the first round of the medley relay event by the United States.