Surrounded by canals on three sides, the massive granite castle is where the queen officially receives guests. From 1441 until the fire of 1795, it was used as the royal residence. Even though the first two castles on the site were burned, Christiansborg remains an impressive baroque compound, even by European standards. Free tours of the Folketinget (Parliament House. 33/37-55-00. www.folketinget.dk) are given Monday through Saturday from June to mid-August, as well as on Sunday from July to mid-August; tours run Sunday to Friday from mid-August through September, and on weekdays from October through April. English-language groups begin at 2. At the Kongelige Repræsantationlokaler (Royal Reception Chambers. 33/92-64-92), you're asked to don slippers to protect the floors. Admission is DKr 60; entry is via guided tour only. Tours are given daily May through September, and Tuesday, Thursday, and weekends from October through April; English-language tours are at 11, 1, and 3. The Højesteret (Supreme Court), on the site of the city's first fortress, was built by Bishop Absalon in 1167. The guards at the entrance are knowledgeable and friendly; call them first to double-check the court's complicated opening hours.

While the castle was being rebuilt around 1900, the Nationalmuseet excavated the ruins (33/92-64-92) beneath it. The resulting dark, subterranean maze contains fascinating models and architectural relics. The ruins are open October through April, daily 10-4, and admission is DKr 25.

Wander around Højbro Plads and the delightful row of houses that borders the northern edge of Slotsholmen. The quays here were long ago Copenhagen's fish market, but today most fresh fish is transported directly from boats to the city's fish shops and supermarkets. However, one lone fisherwoman still hawks fresh fish, marinated herring, and eel in the early morning. She is the last fishmonger you'll see carrying on the tradition.