Most of the gamers only test the GPU through Furmark while buying, and if your cards are passing the stress test of Furmark, I think you're good to go. However, if you can somehow test the "GTA V (five)" (yes, the newer version of same old Grand Theft Auto) with highest possible resolution (of the game) in your system, it'll be the real test for your GPUs (especially of the cards till RX 200 series) in every possible way (stress, temperature, memory, etc). Play it for an hour, run to the Vespucci Beach (in the game of course), and see if everything's fine there. 
This is the process I usually follow as well before selling a used GPU. There are several "gaming" benchmarks out here, I usually use 3DMark, but any that stress the GPU are good. I usually flash BIOS back to original and fire up a benchmark and if it passes the highest test relevant of the GPUs capability I considered it stable. Some benchmarks allow multiple passes, I sometimes will run through 3 loops if I have any doubts, but even one should expose any flaws.
Also make sure you give the cards a once over with a vacuum or air duster to remove excess dirt/dust and check the function of fans as other have suggested.
I also usually state right in the listing that I verified functionality with 3 runs of Firestrike (or whatever benchmark you use) to help minimize the it didn't work type of buyer. I have had a few have buyers remorse cases and after explaining the process I go through to check each GPU for full functionality before shipping they usually reconsider their request.
The highest grade of CPU I have is an i3 processor. It seems the type of CPU affects your score on 3dmark. So if I have a crappy CPU, does it mean it won't test the GPU to its limit and it might seem fine for me but for someone with an i7 which takes the GPU to its limit, it might have issues?
I'll try the Firestrike since there is a demo version I can download. The GTA 5 would be good but since I am never going to play the game, I rather not spend any money buying it.
Does the Firestrike stress the GPU enough to cause artifacts or do you need an actual game to detect artifacts?