It's all cookie-based. You can add items to your basket and and as long as you don't delete the pertinent cookies from that browser, the stuff in the basket stays until you check them out (again, as viewed from the browser from which they were added).
Wouldn't work for me. To clarify with a concrete example: I have two Amazon wishlists. One of them has about thirty five items on it, and consists of the items I'll probably be ordering in the near future. The other has about 250 items, some of stuff I intend to order but not very soon; some of it stuff I sort of want, but may never order, and meanwhile want a convenient place to keep track of; some of it recordings I simply want to remind myself about; and some I will order if the price ever goes down to a level I can live with. My wishlist with Arkivmusic is much smaller but similar. When I order from them, I pick out what I want, but I never order the entire wishlist.
It's not necessarily a problem when they have a sale on a specific label or group of recordings, because they keep those together on one page. But they now have a sale on most of their box sets, and you have to hunt through different pages to track down each individual box set. Which is a pain because I will need to do it twice for whatever I order--once to get the price so I can comparison shop, and then again to actually order whatever I end up ordering from them. At the moment I have a list on paper sitting by my computer--and since I plan on ordering a bunch of Gardiner's Bach cantatas (I have enough of that cycle already to know I want the rest) before I order any of those box sets, I can't resort to your method.
You can't create an account with them, so how do you expect them to let you track your orders at their website? For convenience, I archive my order confirmation and dispatch e-mails at my end.
Every email I get concerning an order stays in my inbox until I get the items, and then is archived, so that's no problem. But other sites (Arkivmusic, for example) have a setup by which you can track the individual order with the order number and your email address without creating an overall account, so I think Presto could do it.
But thank you for at least confirming that it wasn't simply me not seeing something painfully obvious.