Does Tophatter offer Reserve pricing?

Yes, sellers can choose to set Reserve Prices.

When a Reserve Price is set, bidding must surpass the specified reserve price in order for the product to be sold. Note, a Reserve Price Fee is charged for all scheduled items, even if the item is unsold at the auction, or is won then canceled or refunded.

Reserve Price can be set in the Pricing section when creating a new product, or from the Products page on existing products.