Now the price ...
The reservation for the route Stockholm-Kiruna or Stockholm-Narvik is the same if you travel with a rail pass.
As you do not have a rail pass for Norway, you will need a standard point to point ticket from the border to Narvik.
If you book early, you get the one-way ticket for SEK 39 (~ EUR 5).
Select "Riksgränsen" to "Narvik".
It's available in the Raildude shop: http://sj.raildude.com
Buy a "SJ STANDARD JUST NOW" ticket. You can't exchange them anymore, but they are cheaper.