Early in the season, Swift reached another milestone in becoming the first player to make 200 appearances for Connacht, when he played against Edinburgh on 16 September 2011. He made a total of 18 appearances in the 2011–12 Pro12, starting each of the games as Connacht finished eighth. On 2 March 2012, Swift became the most capped player in the history of the Pro12/Celtic League, playing in his 140th game in the competition. Swift made his first appearance at the very top level of European club rugby on 11 November 2011, when he started against Harlequins in the 2011–12 Heineken Cup, a game which Connacht lost 25–17. He also started against Toulouse both home and away, but did not feature in either of the games against Bath, with Connacht losing on each occasion. Swift started against on 20 January 2012, however, with Connacht managing an upset, beating Harlequins 9–8 in the Sportsground, preventing the Premiership club from topping the group, and knocking them down into the Challenge Cup.