May was named the Western Water Polo Association (WWPA) Player of the Week after totaling 10 goals, drawing 16 ejections and five penalty shots, and posting four steals in the team's four games.
The senior helped lead Santa Clara to a perfect 4-0 record with wins against then No. 13 Harvard, No. 14 Bucknell, No. 20 Wagner and St. Francis.
May had three goals in Friday's 15-13 win over Harvard, but saved his best performance for the tourney finale, scoring twice, drawing five kickouts and two 5-meter penalties in Sunday's 15-14 overtime win over Bucknell.
"Reilley was a force at 2-meter throughout the weekend with a lot of production and forcing other teams to drop," head coach Keith Wilbur said. "He was key to the last two goals in the Bucknell game. He scored in the first overtime and drew the penalty shot for the winning goal."
He became the school's all-time leader (200) in earned ejections in Saturday's 9-7 win over St. Francis.
May earned the weekly honor for the second time in his career. He was the WWPA Player of the Week on Sept. 13, 2017, for his performance in the Princeton Invitational.
After winning five of their last six, the Broncos (9-9) entered this week's Collegiate Water Polo Association (CWPA) ranking in a tie for No. 15 with Harvard.