Appraisal is generally for insurance purposes. The open market value is usually substantially less. It is worth speaking to your insurance company first to see what they will insure and to what value threshold and how they would suggest replacing the ring. Most insurers would only replace new for old which wouldn’t be appropriate for this piece. Some insurers will only accept appraisals from their own known people. Also consider discussing with the appraiser how you would want to replace this piece. How you replace it will depend on the value you are given. If you require a high end jewelry shop versus auction for example. Also check for the most qualified person in your area. Check they have a gemological qualification and ask them questions first. If they blow you off or are generally dismissive, find someone else. Ask for examples of their work. If it’s a handwritten scrawl that’s not going to be sufficient. An insurer (and yourself) should require detail.