Ok, since your option sticker is missing, you can try this...
From what I am seeing in the PET for 2001 (page 387), your car will have an immobilizer control unit with one of these two part numbers:
986.618.262.01 (M531 - no keyless entry)
996.618.262.03 (M535 - keyless entry)
To determine which one you have, you'll need to remove the drivers seat and check the part number on the control unit which is bolted to the floor under the drivers seat.
If your car has the .03 part, then I think it's just a matter of buying a new key and having the dealer program the car to accept it. Still not cheap (around $200) but a lot cheaper than adding keyless to your car if it never had it.
Here's an ebay seller with a 3-button fob that should work if you have option M535:
Porsche Boxster 2001-2004 and 996 Targa Key remote | eBay
Not saying you should buy it from them, but that's what you should be looking for.
I can't imagine it would cost a lot more than that from the dealer.
Again, all this is moot though if your car didn't come with the option code M535 control unit.
Hope this helps, or at least gets you pointed in the right direction...
Bill