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Join Date: Sep 2009
Location: Minneapolis: DL DM charter 2.3MM
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Posts: 100,368
Some of the visa service agencies seem to have ways to arrange for the invitation letter, for an additional fee of course. It might seem a little dodgy.
My instinct would be to first try to get the invitations through your hotels, assuming that you have reservations in higher category places that appear to be competently run and regularly have foreigners as guests. Don't try this if you're staying in a hostel or budget accommodations. Expect the hotels to charge a fee for this service.
BTW, with a USA passport, you wouldn't have had a visa for Scandinavia. You may be thinking of getting your passport stamped upon arrival.