Professor Winston is a Faraday Medal holder from the Royal Society and has had many other prizes including a Wellcome Senior Research Fellowship 1973-77, a Blair-Bell Lectureship RCOG, 1978, the Cedric Carter Medal and the Victor Bonney Triennial Medal for contributions to surgery, Royal College of Surgeons of London, 1991-1993. He was Gold Medallist for the Royal Society of Health in 1998. He won the Edwin Stevens Medal (the Royal Society of Medicine) in 2003, was the North of England Zoological Society‘s gold medallist in 2004 and won the Al Hammadi Gold Medal at the Royal College of Surgeons of Edinburgh, 2005. His film, Microsurgery of the Fallopian Tube won best film award at the American Fertility Society 1978, and his teaching tapes series Infertility, Surgery and IVF won awards at the International Federation of Fertility and Sterility.

Robert Winston is a Fellow of the Academy of Medical SciencesQueen Mary College, the Royal Academy of Engineering, the Society of Biology, the Royal College of Surgeons of Edinburgh, the Cities and Guilds Institute and the Royal College of Physicians and Surgeons of Glasgow. He has received twenty honorary doctorates from universities across the world and has been a visiting professor at a number of American, Australian and European universities.

He was President of the British Association for the Advancement of Science in 2005 and was until recently a member of Council of  Engineering and Physical Sciences Research Council and Chairman of its Societal Issues Panel. He is Chancellor of Sheffield Hallam University and on the Council of the University of Surrey