The British actresses, who have have starred in a number of films together, were made doctors during a special ceremony at the Royal Conservatoire of Scotland in Glasgow.
Thompson says, "It's our best starring role together, definitely. We've not received anything like this before and we both feel slightly fraudulent because when I told my son, he asked, 'How many essays did you have to write to get that?' So we feel really lucky that we now get to put 'doctor' in front of our names and pretend we're important."
And the Brave star admits her husband, alumnus Greg Wise, is slightly bitter about her new title: "Greg graduated from here in the '80s or '90s and he's fit to be dead and spitting feathers (mad) at home because he had to do so much work and exams to get his degree and we just had to turn up to become doctors."
Meanwhile, Law, who was born in the city, adds, "It's great fun to be able to do this together, much better than collecting it on your own and to get it in Glasgow is great."