[Mad Tam McC]

Whole fingernails, or just clippings?

Like anything organic they'd decay over time. They could be preserved in a liquid, but that would evaporate.

The best way would be embedding them in a liquid that turns to a transparent solid, a bit like amber (shades of Jurassic Park here!)

Can't be actual amber because it is fossilised, unless there is a way of creating it. Don't know if your world is high tech or magic.