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. Please note, a Reserve Price Fee is incurred each time an item is scheduled into auction, whether or not the item is sold, 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.