For about as long as coins have existed, people have kept them as souvenirs and worn them as jewelry. And for good reason. Coins often have beautiful and artistic designs, are made of bright, shiny metal, and usually carry symbolism relating to the traditions and culture of the country where the coin was struck.
Coin-based jewelry is evaluated at jewelry, not coins. Coin-based souvenirs and keepsakes are evaluated as novelties and gifts, not coins.
Though you mostly see gold and silver coins mounted as jewelry and keepsakes, you sometimes encounter base metal coins mounted in decorative settings. A few examples are shown in our picture. A ring that closes around a coin without damaging it for mounting it in a necklace or such is referred to as a bezel. Non-precious coins are sometimes mounted in silver or gold bezels, which can make the bezel more valuable than the coin itself!
The coins shown in our image include a colorfully painted US cent dated 1908. It was sold on eBay in June 2014 auction for just under $6 US dollars. A similar coin of the same date in the same condition, without the paint and the bezel, would be worth a bit more than that. This is primarily due to the paint detracting from the value. A non-painted coin could just be removed from the bezel, and would sell for about the same as a non-bezeled coin as long as the bezel did no damage (most of the time bezels inflict damage). The other coins shown in our picture, including those surrounded by aluminum rings, called 'encased coins,' sell at similar levels, almost always under $10.
In other words, if you have a coin mounted in a non-precious bezel, and the coin has not been damaged, holed, or soldered, then it's worth the same as a non-bezeled coin.
If the bezel is made of precious metal, and again the coin has not been damaged, then you can simply add the value of the coin to the value of the bezel.
Sometimes, scarce old copper coins are sold in beautiful aged silver bezels. These may bring in a small premium from a collector who wishes to purchase the item as a combined jewelry piece. This is a slightly 'fringe' area of coin collecting, and any such premium will vary widely depending on the sales venue and the buyer.