Some ways to sell silverware include bringing it to a silver collector, visiting a road show for silver items and bringing it to a local antique shop. There is also the option of selling it to pawn shops for quick cash, though this isn’t recommended for vintage items.
The smart thing to do before selling silverware is to have it appraised. This gives more information about what the silverware is worth and whether or not it is a vintage or antique silverware set. If it is antique and brought to a pawn shop, it is only going to be purchased based on the weight of the silver in most cases. The person selling the silverware gets much less than what it is worth. Some good organizations that provide lists of reputable appraisers include the International Society of Appraisers and Appraisers Association of America. The appraiser might also have suggestions for reputable dealers.
Selling silverware to collectors or private dealers is another good option. Instead of choosing a dealer or collector of different types of items, try to find one that buys silverware and related goods. They are more specialized with this type of item, know what it is worth and typically are more willing to pay what it is worth.