My grandfather died in Glasgow in May 1938. Is there any way I can see his Will?
Likewise my grandmother who died in Glasgow in 1947?
This is a yes .... but ....
The information on the page
Mckha has quite correctly referred you to is fine if you are doing the research in person and in-house, but it doesn't tell you the full story if you want to get the documents from afar.
For this period, you start by consulting the Calendars of Confirmation (don't look for 'probate' as there is no such procedure in Scots Law). These are printed tomes, one for each year. They list alphabetically by surname all confirmations
granted in that year, so although most are confirmed within a year of the death it is quite common to have to look through several volumes, starting with the year of death, to find the one you want.
The Calendars are available in some public libraries in Scotland, or in digital form in the Historic Search Room in the National Records of Scotland. You need to have a reader's ticket for the NRS to use the latter.
Once you know the date and the court where the confirmation was granted, you consult the in-house index at NRS to get the catalogue number for the volume containing the court and date you are interested in, and you order that volume.
However many (most)? volumes of wills and testaments are not stored in the same building as the Historical Search Room, so you have to place your order and come back a day or two later to see the volume.
If you want a copy of it you have to order it in the search room, and it will arrive in due course by post. There is a charge for photocopying. (They probably have plans to continue digitising wills and making them available via the SP web site, but that isn't imminent as far as I know.)
So if you have a reader's ticket and you can spend a day or three in Edinburgh, it's easy enough to do but takes a bit of time.
There are two possible ways of getting these wills without going to Edinburgh.
One is to contact the NRS using the contact form on their web site
https://www.nrscotland.gov.uk/about-us/contact-form giving them the names and exact dates of death, and ask them to find, copy and send you the wills. They will charge you for this service and for the photocopying, and it could take a few weeks if they are very busy.
The other is to hire a professional researcher. See
http://www.asgra.co.uk/ which could be quicker but you would have to pay for the researcher's time as well as for the copying. I do not know, never having done either, whether a professional researcher's time would cost more than the NRS's own search charge.
Don't forget that they may not actually have left wills at all.