It appears from Google Earth and a Copenhagen bus transit map that bus #26 goes from the port (LANGELINIEKAJ Pier) to Tivoli Gardens, but also makes a stop near Rosenborg Castle (Sølvgade (København)). The RS Northern European Cruise Ports book doesn't mention this as an option for getting to Rosenborg Castle. Can anyone confirm that bus #26 does stop near Rosenborg Castle?
I believe I answered my own question with the help of this web site --- http://www.rejseplanen.dk/.
It's a five minute ride via bus #26 from the Indiakaj stop at the port to the Sølvgade (København) stop and then a less than five minute walk to to the castle. It seems to me that this would be quicker than the Metro.
We also plan to get back on #26 and ride it to Radhuspladsen and then walk back to the boat via RS Self-Guided Walk
If you're looking at a Cruise Ports guide. I'm assuming you're coming from a cruise.
Rosenborg is a good choice; the small palace upstairs, the crown jewels in the basement, and the surrounding park make a nice visit.
Our cruise was docked up near Nordhavn. If you're in the same area, you can catch a train to Norreport (I think two stops). Rosenborg is a really short walk back north from there.
To get out of the port, follow the blue line painted on the ground. That takes you to the gate, from there cross a street then under the tracks, turn left and you will see both bus stops and the train station.
When you're done at Rosenborg, you can walk west to Amalienborg, Nyhavn, Kongens Nytorv and/or the north end of the Stroget. There is a lot to do in this area or follow the Stroget south to the City Hall, Museums, and Tivoli.
Looks like you're on the right track. Happy planning!