Try searching for deaths on ScotlandsPeople using their names, and your grandmother's maiden name, as for deaths after 1974 the mother's maiden name was recorded. After that it's a matter of cross-referencing their age at death with their birth year, and eliminating those that are not close. Female deaths are also usually registered under both their maiden and married names, if they married, so it can also give you clues as to possible marriages. You won't be able to view the details because you will run into the statutory limitations on viewing the information (75 years for marriages, 50 for deaths), but it will allow you to draw up a short list of possible candidates and potential places that they lived. Hopefully what I have told you doesn't violate Rootschat's no living persons policy, but it will allow you to go a little further.
Family trees on Ancestry are also a good resource. I know that my father has a living cousin because of a family tree I found on Ancestry a couple of months ago, but frustratingly the person that started it hasn't logged into Ancestry for almost a year now. I have, however, found someone from my grandfather's father's family which was nice, so I now know a little more about his half-brothers and sister on that side.
