As an undergraduate, Robert Watson was an eastern intercollegiate wrestling champion in the 175 pound weight class. After graduating from Lehigh in 1913, Watson went on to join a law firm in Washington, D.C.: Watson, Cole, Grindle and Watson. With the exception of his service as United States Commissioner of Patents under President Eisenhower from 1953 through 1961, Watson spent most of his career with the D.C. firm.
In 1958 Watson was awarded the Jefferson Medal of the New Jersey Patent Law Association as well as the "Charles F. Kettering Award for Meritorious Work in Patent, Trademark, and Copyright Research and Education George Washington University. Watson served as president of the American Patent Law Association as well as chairman of the Section of Patent, Trademark, and Copyright Law of the American Bar Association which awarded him an honorary LL.D. in 1954. He received the "L-in-Life" award from the New York Lehigh Club in 1960.