Instructions
Test the depth of the engraving and the thickness of the piece by placing your fingernail in the groove of the engraving and rubbing. If you notice waves on the back of the piece as you do so, the piece may be too thin to withstand the removal process without being damaged. This is especially true for silver trays, thin rings and hollow pieces.
Take a less valuable piece of the same material, for example a damaged silver spoon, to the smith you are thinking of hiring. Testing the skill of the smith on a less valuable piece will prevent you from having your valued possession damaged by incompetent workmanship.
Ask your smith about laser welding. The Society of American Silversmiths names laser welding as an effective technique for filling in an engraving. Using a smith who is proficient in laser welding will decrease the chance that your piece will be damaged.