I've looked at a few reports and most of the mentioned species are connected to marshes/bogs and/or mountainous areas from just below the treeline to well above. If I were to go, I would probably try first at heights between 200 and 500 metres (south facing slopes). But, as Finnmark may be considere...

Hi Mark! I live a bit further south in Norway, so I have no personal experience with butterflies in Finnmark but the general consensus seems to be that the town of Alta is a good place to set up base camp. This area should give you a chance for species like: Freija Fritillary (Boloria freija), Alpin...

Second and third looks like Purple-barred Yellow:
http://www.ukmoths.org.uk/show.php?bf=1717