The Pegasus Cup was donated to CUCBC by Richard Naisby of Milton Brewery in 2006. The Cup is awarded to the most successful Boat Club competing in the May Bumping Races. To be eligible to compete for the Cup a Club must have at least one men's and one women's boat entered in the May Bumps (excluding the Getting on Race) or, in the case of single sex colleges, at least two boats entered. The Cup is awarded to the Club gaining the most points over the course of the May Bumps. Points are awarded as follows:

1. One point for every place gained by each of a Club's boats.
2. One point for each night that a Club retains the Men's or Women's Headship in Division One.
3. One point deducted for every place lost by each of a Club's boats.

The total number of points gained over the four days of racing is multiplied by 12 and then divided by the number of boats entered by the Club to give the final score.