If you don't want to do a specific gravity test, if you have a calipers or similar you can measure the thickness and diameter of the coin. You can get a pretty good estimate of the volume to calculate the density of the coin. Gold is so much denser than silver or copper alloys that it should be clear which is plausible.
In theory... right? But it seems all of these medals are brass, then silvered or gilded afterward. So I don't think that would work, would it?
The layer of gold or silver would likely be so thin as to have a negligible effect on the density. A much bigger affect would be if the gold were not a pure alloy. Gold is more that twice as dense as copper (~19 g/cc vs ~9 g/cc). So even a fairly simple test can usually confirm if something could not possibly be gold.
Well, I tried testing out my idea of calculating composition from volume and weight. It didn't really work. For a zinc penny I calculated a volume of 0.421 cc and weight of 2.49 g for a density of 5.9 g/cc. Zinc has a density of 7.13 and copper of 8.92. The weight is fine (2.50 g on Numista) so the volume must not be accurate enough. Any density measurement outside the range of the two constituent metals is a garbage result and can't be used to estimate composition. Maybe the thickness measurement isn't accurate enough to be useful due to the relief texture of the coin. Maybe wear throws it off. Anyway, don't take my advice--specific gravity measurement is much more accurate. You could probably tell the difference between gold and silver or copper by estimating the volume because the difference is so huge, but for any metals close in density like copper and zinc it's not practical. Oh well.