[swarmee]

They base it on previous sales captured in their Auction Prices Realized tool, and possibly based on SMR. If there is none of the same cards in the same grade, they may look at lower grades and then prorate to a higher valuation. It's completely up to them, although a Blowout poster has said that he was able to get them to reconsider when he showed them more recent sales for cards like modern basketball that shot through the roof and then dropped 75% from the peak.

Officially, they don't offer drop-off unless you're taking it to a card show like The National where they are bringing their slabbing machines. However, they did post on Twitter when they let Phil Hughes bring his cards in, but he's a player and internet celebrity, so it's not for the common folk. You may have a better chance if you get an auction house who does plenty of business with PSA to help you broker this sale.