In 2011, McVeigh was appointed co-captain of the Sydney Swans alongside Adam Goodes. The death of his newborn daughter, Luella, marred his season. In his absence, the Swans defeated eventual premiers at Skilled Stadium (the first time a visiting side had won at that location in four years) in round 23 and dedicated the win to the McVeigh family and Luella. Despite such a tragedy, he managed to finish 10th in the 2011 Skilton Medal. In 2012, McVeigh captained the Sydney Swans to the 2012 premiership. His strong year was rewarded with a fifth-place finish in the 2012 Bob Skilton Medal. In 2015, McVeigh became only the seventh person to reach 250 games for the Swans in round 7.