In 1973 Klass was named a fellow of the Institute of Electrical and Electronics Engineers. He also was a member of the American Association for the Advancement of Science, the now-defunct Aviation/Space Writers Association, the National Press Club, and the National Aviation Club. Asteroid 7277 (1983 RM2) was named "Klass" after him. He received the Lauren D. Lyman Award in 1989 from the Aviation/Space Writers Association for distinguished career-long achievements, and the Boeing Decade of Excellence Award for lifetime achievement in 1998 from the Royal Aeronautical Society.