...my sim card never worked outside of Iceland and yesterday I went to Siminn to fix this. Coming into the shop I was first of all dumbfounded by the fact that they wanted me to type in my kennitala to get a number to be served. One of the attendants saw my confused face and I told her about my errand. For some reason a credit card was needed to make my sim card work abroad and as luck had it I even had mine with me. But as it was not an Icelandic credit card I suddenly ended up in a Little Britain sketch.
I thanked the (to her credit flustered) attendant, went out of the shop, into the adjacent phone shop (Nova), took a number by pressing a button, asked for a prepaid sim card which works abroad, got one, paid and left without ever having to give a kennitala, Icelandic credit card or anything else.