It will depend on what you are trying to learn from your appraiser. Unfortunately, ‘worth’ is not a fixed number and will vary from market to market. It’s a reasonable question to ask what a high end guild type store would charge to custom make a ring like the one you have but this is not the same question as asking what you can reasonably expect to receive from a pawn shop.
Many buyers are trying to decide if their dealer has given them complete and accurate information in the sales presentation. This is a valid concern and, if this is the case, a statement by the seller doesn’t really help very much. If you are satisfied that you got what you paid for and are seeking documentation for purposes of binding an insurance policy, seller supplied reports can often be entirely sufficient.
It’s a mistake to decide on the merits of an appraisal based on the bottom line number presented. Each appraisal should be addressing a specific question or ‘purpose’. If the purpose is to bind an insurance policy, the most important section is the description, not the price. In the case of a loss this description will be used as a purchase order to buy you a replacement. Read it carefully to be sure it contains all of the details that you consider important about your piece. The bottom line number is the maximum liability for the company. It’s doing no favors to make this higher than what will be required for the company to make a replacement because it increases your premiums without changing their behavior in the case of a loss.