A few thoughts:
- Even though your aunt bought the watch for $37k, she should have it reappraised by a certified Piaget jeweler/dealer. A proper appraisal will help her get fair value and temper expectations. Most likely she is greatly overestimating what someone will pay. Or heck, maybe she has the rarest watch on the planet and it's worth a fortune. You should know either way.
- Selling to a jeweler/dealer will get the lowest amount because he has to flip it and make a profit, but it's zero fuss.
- Selling on eBay should be taken seriously. If you don't already have an active account with dozens (if not hundreds) of transactions and a positive feedback score, you need to sell other, smaller, less expensive things to learn the ropes. Crooks scour eBay looking for people who don't know their tricks selling big, expensive items.
- If you sell on eBay, use their escrow service (escrow.com) for the transaction. This will lessen the chance of fraud and scare off most criminals. Don't use ANY OTHER service. The bad guys set up fake escrow services to defraud people.
- Realize everyone gets a piece of the pie. eBay will get fees, the escrow company has their fees, shipping by verified carrier with tracking and insurance costs money... Prepare Auntie to share the take.
- Taxes, taxes, taxes. Oh yeah. And if you sell it via eBay, taxes must be paid. Whoever owns the account will receive a 1099 at the end of the year and Uncle Sam wants his cut. Make sure Auntie sets aside enough to pay that bill.
Good luck.