Back from a long weekend in Copenhagen and we did try one the two Michelin star restaurants recommended -
Kong Hans Kaelder Keller. The atmosphere and the staff were fantastic and even if the food was not the sort you'd remember in a years time, there was nothing to complain about either. We had their menu innovative, accompanied by their choice of wine by the glass per course. In all, I thoroughly enjoyed the whole experience and if price is not an issue, would recommend it highly.
Aside from that, most of the other restaurants were only adaquate (a lot of fish, some good open sandwiches and the ubiquitous herring), with very casual service and the city itself is expensive.
A great place for a long weekend though and a lovely old city.