Williams was drafted by the Chicago Bears in 1959 (coincidentally, he was the second Notre Dame QB with the name "Bob Williams" to be selected by the Bears during the same decade), but instead he chose to enroll at the University of Pittsburgh School of Medicine. He was inducted into the Pennsylvania Sports Hall of Fame in 2002.[2] His son Brian Williams played center for the New York Giants from 1989 to 1999. His grandson, Maxx Williams, is a tight end who was drafted in the second round of the 2015 NFL draft by the Baltimore Ravens.