I have missed a connection in Keflavik! Our flight from Munich to Keflavik was delayed. We arrived in Keflavik with 10 minutes time remaining and prepared to run. As we approached the gate on landing, our phones started going off and telling us that Iceland Air had rescheduled us for the same flight the next day. There were a good 20 some people in the same situation. Our only option was to go to customer service where they cheerfully gave us hotel, transportation, and meal vouchers and a brochure on how to apply for EU compensation.
Our hotel was fine, meal vouchers sort of worked, and transportation worked as well. We made it home a day late. It cost just under $400 to change final flights home by a day. This was later reimbursed by trip insurance. Each passenger did receive 600 euros in compensation.
It worked out okay for us to be delayed by a day, but it sounds as if that might not be the case for you.