Peters was appointed a Member of the Order of the British Empire (MBE) for services to athletics in the 1973 New Year Honours. For services to sport, she was promoted in the same Order to Commander (CBE) in the 1990 Birthday Honours and again to Dame Commander (DBE) in the 2000 Birthday Honours. In the 2015 New Year Honours, she was awarded as Member of the Order of the Companions of Honour (CH), also for services to sport and the community in Northern Ireland, and in 2017, she was made a Dame of the Order of Saint John (DStJ). Peters was appointed a Lady Companion of the Order of the Garter (LG) on 27 February 2019.