Premii obtinute de Stephen de-a lungul anilor

• 1975 Eddington Medal
• 1976 Huges Medal of the Royal Society
• 1979 Albert Einstein Medal
• 1981 Franklin Medal
• 1982 Order of the British Empire (Commander)
• 1985 Gold Medal of the Royal Astronomical Society
• 1986 Member of the Pontifical Academy of Sciences
• 1988 Wolf Prize in Physics
• 1989 Prince of Asturias Awards in Concord
• 1989 Companion of Honour
• 1999 Julius Edgar Lilienfeld Prize of the American Physical Society
• 2003 Michelson Morley Award of Case Western Reserve University
• 2006 Copley Medal of the Royal Society
• 2008 Fonseca Price of the University of Santiago de Compostela
• 2009 Presidential Medal of Freedom, the highest civilian honour in the United States