Montag became the chief physician for the German Ice Skating Union, and the German Ice Sport Federation in 1972. In these roles he oversaw medical concerns for figure skating events hosted in Germany; which included the 1973 European Figure Skating Championships, the 1980 World Figure Skating Championships, and the 1983 European Figure Skating Championships. He was the team doctor for the West Germany men's national ice hockey team, and the primary physician for West German athletes at the 1972, 1976, and 1980 Winter Olympics.