Hi Jack - welcome to Rootschat.
Robert may be mentioned in the burial records at Stewarton and/or in Monumental Inscriptions lists. I'm not sure if either are available online; someone may be able to advise you better! There won't be a death certificate (or entry) for him, but sometimes cause of death and other details are mentioned. It just depends how detailed they kept their records.
In Scotland, a woman always retained her maiden name. She would use her husband's name for census (with exceptions too), but on parish records, nearly always are they mentioned with maiden name. If their husbands pre-deceased them, it was quite often they reverted to it (possibly using it when re-marrying). My own 3x great-grandmother did this in 1876 (as did my other 3x-gg in 1852).
Hope this helps.
hume
