I stopped in Amalienborg since it was free with my Copenhagen card. I don't think I would recommend it otherwise, unless you really love royals and historic buildings.
There are lockers as no bags are allowed (not even large purses). Get your Copenhagen Card ticket at the gift shop down the stairs, drop your bag, and head up.
The display is quite static, with the space through which you walk the rooms encased in plexiglass. You start in the post-WWII era, and walk back in time, going back 100+ years. Each room is decorated as the royals of the day had it; one even has a photograph of what it looked like showing the similarity to how it is currently displayed. Many rooms had every inch covered with tchotchkes, particularly the more recent ones. The hallways between rooms also had pictures and displays.
The second floor has much less to see, but I was intrigued by the Order of the Elephant. Why Denmark would've chosen the elephant for its royal order 400 years ago was never explained.
There are a few docents who can answer questions, but much is contained in the text display (Danish and English). Didn't take all that long, though I didn't read every word - I'd say about 45 minutes. read more