Grace Fewell is a marketing manager whose veneers fell off the night after she got them placed. Veneers are glued on top of real teeth, and should last 15 to 20 years before needing replacement.

Many of us will lose an adult tooth in our lifetimes, whether through disease or misadventure – a punch that landed, a skateboarding trick that didn’t, say. And if you join these ranks, which include ...