R.C. Stevenson was a recipient of the Nathaniel G. Herreshoff Trophy by the North American Yacht Racing Union in recognition of his work in establishing junior sailing and racing programs in Canada, the United States, and for Olympic class fleets in Canada.

In his honour, The Trophée R. C. Stevenson Trophy is awarded for the Flying Dutchman boats. The R.C. Stevenson Memorial Boat loan fund was established in 1982. A past commodore of the Royal St. Lawrence Yacht Club, the purpose of the funds is to assist Canadian Yachting Association member clubs in the purchase of sail boats to be used for junior training.

Stevenson was inducted into the Canadian Olympic Hall of Fame in 1971.