Shaw appeared on the cover of "Sports Illustrated" magazine on August 4, 1975, after receiving the FINA Prize Eminence Award in 1974, representative of the greatest contribution to world aquatics. He was named World Swimmer of the Year in 1974 and 1975, and won the Sullivan Award in 1975 as the most outstanding amateur athlete in the United States after having won three gold medals at the World Aquatics Championships. In 1989 he was inducted into the International Swimming Hall of Fame. In 1991, he was inducted into the USA Water Polo Hall of Fame.