Most appraisals are done mounted. Some people will want to have their stone inspected loose and then again after setting but if we’re talking about a new purchase of a lab graded stone and you’re only going in once, I recommend going after the piece is finished. This allows the appraiser to inspect the craftsmanship of the mounting, to take the photographs of the finished piece and to prepare documentation of what you have. If it’s something other than a new purchase and/or something other than insurance then it’s going to depend on what you’re trying to accomplish. Some times you’re better off loose, some times your better off mounted, some times you’ll want both.