Dr. Gillespie's Collection of Awards
- Fellow of the Royal Institute of Chemistry, 1953
- Fellow of the Chemical Institute of Canada, 1960
- Fellow of the Royal Society of Canada, 1965
- Noranda Award (Chemical Institute of Canada), 1966
- Canadian Centennial Medal, 1967
- Union Carbide Award (Chemical Institute of Canada) for Chemical Education, 1976
- Silver Jubilee Medal, 1977
- Chemical Institute of Canada Medal, 1977
- Fellow of the Royal Society, London, 1977
- Tory Medal (Royal Society of Canada), 1983
- McMaster Students Union Award