Most of these coins are truly exquisite. Many come in full color, like the examples in our picture. These are modern medals produced for any of a host of people, events, and places to capture and commemorate military service.
One of the biggest producers of challenge coins and related medallic art is the Northwest Territorial Mint in Auburn, Washington, USA.
Carol's coin is clearly from the NWT Mint, and it also contains one troy ounce of gold. As such, it is a very valuable piece.
Here is how values run for these coins. However, it must be noted that most of the value in these coins is due to sentimental reasons, and that value is not quantified here. These values are the cold and dry result of precious metal content, artistic endeavor, and manufacturing cost (how boring!).
COINS WITH PRECIOUS METAL - The value is a few US dollars more than the value of the silver or gold. At the moment, gold is trading at $1656 US dollars per troy ounce, so Carol's coin is worth about $1690 or so. Silver is at $30 per troy ounce. Look up the current value at kitco.com because it changes constantly.
COINS WITH NO PRECIOUS METAL - Copper, brass, steel, pewter, and similar metals do not add value. These coins sell retail for $5 to $25.
If you have coins like this to sell to a dealer, figure he or she will offer about one-half the retail price, more if precious metal is involved. Such wholesale to retail mark-ups are necessary to keep the dealership in business.