Amalienborg and Rosenborg

I've only visited Rosenborg, but going at a leisurely pace, I recall it took me perhaps 40 minutes or so. I've been to so many of these palaces over the last decade that they're starting to become a big blur, but I believe Rosenborg more or less functioned as a display for many of the valuable knick-knacks the Danish monarchy had accumulated throughout the ages, especially the crown jewels. Not so much of an attempt to replicate the historical living quarters of the monarchy. My memory might not be 100% accurate on this, though.

Rosenborg is nice, it's small. I think a little under an hour for upstairs and maybe another half hour for the crown jewels in the basement is plenty. You might want to spend a little more time walking around the surrounding park (good picnic choice).

I went under but not in Amalienborg, there are foundations of the castle that preceded the current palace. Modern palaces aren't my thing. I think you can skip the foundations underneath, they're at best marginally interesting. There is a changing of the guard ceremony that takes place out front, we watched that for fifteen minutes or so.

For the history buff, the National Museet, downtown, is really good - lots of Viking and medieval artifacts.