An appraiser will charge a fee. He will also give you a written appraisal on his letterhead and sign it. It should stand up in court.
For jewelry start with the people you bought from. They may also give you a cash value offer. It will be less than you originally paid. He has a business to run.
Same with artwork. Go to the gallery you bought from. Some galleries may help you consign to high end firms. They will get a finders fee from this. They should tell you this up front. The amount is none of your business but is usually about 10%
For eBay sales ask for an insurance value appraisal. This will be higher that what you will get here. If you are settling an estate ask for an estate appraisal. This will be about what you will get on eBay or at public auction
Watch as many episodes of Antiques Roadshow as possible sung attention to to value at original broadcast and the current value.
