Han var gift med Norma Agnes Scholan fra 1968 til hendes død i 2004.<ref name=whoswho>{{Who's Who | surname = STODDART | othernames = Sir (James) Fraser | id = U36360 | volume = 1997 | edition = online [[Oxford University Press]]|location=Oxford}} {{subscription required}}</ref><ref name="Award">{{cite web|title=Alumnus Presents New Prize for PhD Students|url=http://www.chem.ed.ac.uk/alumni/get-informed/newsletter-issue-5/alumnus-presents-new-prize-phd-students|access-date=27. maj 2016|website=University of Edinburgh}}</ref><ref name="Scotsman">{{cite news|title=Norma Stoddart (Obituary)|url=http://www.scotsman.com/news/obituaries/norma-stoddart-1-513988|access-date=27. maj 2016|work=The Scotsman|date=16. februar 2004|archive-date=25. december 2018|archive-url=https://web.archive.org/web/20181225232730/https://www.scotsman.com/news/obituaries/norma-stoddart-1-513988|url-status=live}}</ref>
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