Shaw was elected as both a Fellow of the Australian Academy of the Humanities (FAHA) and of the Academy of Social Sciences of Australia (FASSA) in 1967, a Fellow of the Royal Historical Society of Victoria (FRHSV) in 1973, a Fellow of the Royal Australian Historical Society in 1979, and as the first Fellow of the Federation of Australian Historical Societies in 1998. In 2002, having sat on the editorial board from its formation in 1960 until 1999, as well as being Section Editor for the first two volumes and contributing ten articles, he was awarded the inaugural Medal of the "Australian Dictionary of Biography".