The 2009–10 season was Bradley's last in charge of the side, and he announced his attention to leave the province early in the season. Swift made 12 appearances in the 2009–10 Celtic League, starting in nine of these games and scoring a try. Connacht again finished in last place. In the 2009–10 Challenge Cup, Swift played in all of Connacht's group games, starting in four and coming on as a replacement in the other two. He also scored two tries against Olympus Madrid. Connacht won all of their group games to enter the knock-out as top seeds. Swift started in the province's quarter-final win over Bourgoin, scoring a crucial try in a three-point victory. In the semi-final Connacht faced a Toulon side featuring Jonny Wilkinson, and were beaten by a score of 12–19. In December 2009, Swift became the most capped Connacht player of all time, overtaking Eric Elwood with 169 appearances.