McCourt won a bronze medal for the Ireland in the 1964 Summer Olympics in Tokyo in the lightweight division. McCourt lost a controversial 3-2 decision to Russian Velikton Barannikov. Shortly after the games, McCourt defeated Olympic champion Józef Grudzień of Poland. A year later, he repeated his bronze medal performance at the 1965 European Amateur Boxing Championships in Berlin in the same grade. In 1966, McCourt won a gold medal, representing Northern Ireland, at the Commonwealth Games in Kingston in the Light Welterweight division. McCourt was rated the number one amateur boxer in the world for four years. A master of defence and counter punching, he is inducted in the Irish Amateur Boxing Hall of Fame.