I hate to try to pick what kids will like. When we took our boys to Europe, I asked them what they wanted to see. They replied, "Castles." I asked whether they wanted to see restored castles or ruins. "Ruins." (maybe your teens speak in more than one word sentences).
I don't know of any castle ruins in Zealand. The closest may be the casemates in Kronborg Castle, a short train ride north from Copenhagen in Helsingor. I think they would also enjoy the cannons and relatively brief tour of the main castle.
Fredericksborg may be the best castle, but the gardens are a big reason for that - not sure your boys would particularly enjoy those.
Rosenborg is in town, walking distance from downtown - easier from Nyhavn. Rosenborg is small and is surrounded by a city park with lots of locals enjoying the area. The castle itself is small and the crown jewels are in the basement. If nothing else it's close and small, so even if the boys don't particularly like it, you haven't invested much in the trip.
There are some ruins from an earlier castle under Amelienborg Palace, but nothing really inspiring. The palace itself probably wouldn't be particularly interesting to teen boys other than possibly the changing of the guard (that begins with a march from Rosenborg).
The boys would probably like the Viking Ship museum. They can even try on chain mail, ax and shield. It's mostly an open air ship building museum. If they like watching people carve wood and build things, they would especially like it. You can also man an oar and go out on the fjord (looks more like a small lake) on one of the boats.
The Cathedral in Roskilde has a lot of tombs. Have them find the bones of Harald Bluetooth - a Viking king from the 900's. They may think that's kind of neat.
Aero seems to be a Rick Steves created destination. Most people can't figure out what the appeal is.
Christiana is essentially a community of hippy squatters. The crafts and sights are exactly what you would expect from a commune or Grateful Dead concert. Other than that there's nothing wrong with it.
A canal cruise is pleasant if not thrilling. If it's good weather, I'd plan to take one. The boys might like the guide narrating the tour in multiple languages. Ours did English, Danish, German and French.
There is a church steeple with the stairs on the outside. I think they offer tours that might be thrilling.
Best museum? If they're interested in Vikings, the National Museum has tons of bronze age artifacts - then goes into the Middle Ages with lots of swords and armor.