Pressman is best remembered as the long-time goalkeeper of Sheffield Wednesday, where he spent 19 seasons, playing 478 matches in all competitions including the UEFA Cup. Pressman signed his first professional contract for the Owls on his 18th birthday in 1985 and made his debut against Southampton on 5 September 1987. He had supported Wednesday since childhood. Pressman's career was nearly wrecked on New Year's Day 1990 when he suffered cruciate knee-ligament damage which sidelined him for over eight months. He was unlucky not to play in the 1991 League Cup Final victory against Manchester United, as he had played in every round of the competition that year as well as a significant number of league matches until the quarter final stage where he was replaced by more senior goalkeeper and future Wednesday manager Chris Turner. Pressman was on the substitutes' bench at three further Wembley finals, all in 1993; the League Cup Final, FA Cup Final and FA Cup Final replay, all against Arsenal and resulting in defeats in both competitions for Wednesday.