Three times he received the highest navy award for noncombat service, the Distinguished Service Medal. He was awarded the American Defense Service Medal with one star, the Asiatic-Pacific Campaign Medal with eleven stars, and many more. On January 7, 1972, Rear Admiral Smith received a high "Order of Chivalry" from Queen Elizabeth II of England. This made him "Honorary Knight Commander of the Most Excellent Order of the British Empire." His technical peers showed their respect by the L. T. E. Thompson Award (1957, Naval Ordnance Test Station). He was also awarded the C. N. Hickman Award (1957, American Rocket Society); the American Society of Naval Engineers Gold Medal (1961); the William S. Parsons Award (1961, Navy League of the United States); the Gold Knight of Management Award (1972, National Management Association); and an honorary doctor of laws degree (New Mexico State University). Levering was elected to the National Academy of Engineering in 1965.