You'll need a SIM card in an iPhone 4S to get Verizon Wireless to work in Sweden.

You may already have it. They found an ICCID number for my phone at Verizon's store and concluded that I had it. Without it you can only hit the default CDMA network for Verizon. That might be spotty in Stockholm. I'm not certain as I haven't been yet. A better thing might be to use other networks and for that you'll really need the SIM (subscriber identity module) card. In advance of a trip, you'll tell Verizon to turn on the roaming capability for a month-long window. Turn the phone off or put it on Airplane mode (kinda the same thing) on the flight over and then go back to using it on the other side of the Atlantic.