Feenstra is a fellow of the American Vacuum Society, and was the 1989 recipient of its Peter Mark Memorial Award. He was elected to fellowship of the American Physical Society in 1997, "[f]or contributions to the development of the Scanning Tunneling Microscope as a spectroscopic tool to probe semiconductor surfaces and surface phenomena," and was awarded the APS Davisson–Germer Prize in Atomic or Surface Physics in 2019, "[f]or pioneering developments of the techniques and concepts of spectroscopic scanning tunneling microscopy."