In the vast majority of instances, the cost of a written appraisal isn’t worth the additional expense. Instead, if the buyer has a concern, consider allowing them to take it to a jeweler for verification, with the option to return it to you.
There are certain cases when you would want an appraisal. The most common examples include
Larger natural (mined) diamonds, typically over 1 carat and a good quality,
Larger gemstones that are of a good quality and more rare, such as sapphires, emeralds, rubies, and alexandrites, and
Designer jewelry from only the highest designers, for example Cartier, Tiffany, Bvugari, among others.