United Airlines is offering San Francisco SFO to Copenhagen CPH for $528.11 round trip through united.com on several departure dates in July. This is about $200 lower than other airlines.
The catch is every itinerary I found required a 10pm-9am overnight in Zurich on the return flights. But still a good deal if traveling as a couple and you can find a hotel deal. There are hotels like Radisson Blu inside Zurich Airport or the train to the city is frequent and convenient.
United Airlines San Francisco SFO – Zurich ZRH – Copenhagen CPH – ZRH (overnight) – SFO
Itineraries with United long-haul each way allows self-selected seats at booking.
United Airlines San Francisco SFO – London LHR – Copenhagen CPH – ZRH (overnight) – SFO