Savage was signed by Manchester City in November 1953, where he deputised for Bert Trautmann. He was at the club for more than a year before making his debut, a 2–0 defeat to Newcastle United on 27 December 1954. He also played in the next game against Burnley, but once Trautmann recovered from injury Savage returned to the reserves. His next chance came in April 1956, when he again replaced Trautmann for two matches. Trautmann broke his neck in the 1956 FA Cup Final, giving Savage the opportunity of an extended run in the first team during the 1956–57 season.