Roskilde, as a former capital is well-worth the excursion from Copenhagen. The dizzying cathedral is a towering structure that should be admired by a full 360 degree exploration of the surrounding grounds. I photographed every corner of the interior, and viewed the cathedral from several different vantage points. During my visit the Summer weather was excellent, so it made the visit that much more pleasant.
The amount of royal tombs/caskets located inside the cathedral itself is surprising. Certain areas within the cathedral are quite different because of the internment of a particular monarch. More prominent personas and the century they died all create a varied interior that is quite different from the monotonous interior of many other cathedrals.
I spent half-a-day here visiting the cathedral and the Viking Ship museum, which is also worth exploring via the forested road directly across from Roskilde Cathedral. I should mention, the Copenhagen card is quite useful for a multi-day visit to Denmark. Trains outside Copenhagen are included, as well as admission to Roskilde Cathedral, and several other important sites in North Zealand.