Harvard celebrated the contributions of Cleary to the Harvard hockey program and USA Hockey with the retirement of the number 4 that he wore while he was a player at Harvard. The rafters of Bright are adorned with a retired number 4 banner to commemorate his contributions to the program. The ECAC named the trophy awarded to the winner of the regular-season title in Cleary's honor in 2002. The Cleary Cup is awarded to the team each season that earns the best regular-season, intraconference record in the ECAC.