Travel by private car to the Rosenborg Castle, once the favored residence of 17th-century King Christian IV, where the paintings, sculpture, objets d'art and decorative weaponry of the monarch are on display. The crown jewels of Denmark can also be viewed here, when they're not in use at state functions. Guided tours of the museum can be arranged in advance.
Spend the second half of the morning contemplating the stunning collection of modern art at the Hirschsprung Museum, amassed by tobacco manufacturer Heinrich Hirchsprung in the late 1800s. This is one of the most comprehensive collections of the Danish Golden Era in the world, and the paintings are presented with care in a setting meant to be intimate and approachable. The neoclassical mansion that houses these works is impressive in its own right, so be sure to notice the design details.
Lunch is at Relae, a recent addition to the New Nordic scene in Copenhagen. The multi-course tasting menu changes regularly, but the dishes are always focused, fresh and flawless. Head chef Christian Puglisi worked at Noma before opening his own restaurant, and the influence of his time there is clearly seen in the playful approach to classic methods. The menu also reflects his Italian background, as well as a stint working at El Bulli in Spain.