The Royal Danish Naval Museum (Orlogsmuseet) in Copenhagen is located close to the harbour, one block away from the Vor Frelsers Kirke. It has a very fine collection of ship models that show the developments in Danish naval technology. Many exhibits refer to naval history of Denmark and Copenhagen, e.g. Admiral Tordenskiold in early 18th century or the battle of Copenhagen 1807.
There is more information on the homepage of the Orlogsmuseet.
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Ship of the line "Dronning Juliane Maria" of 1752, 1 : 36 scale contemporary model
Just 300 m from the Orlogsmuseet there is the Vor Frelsers Kirke, built in 17th century. In August 2009, when I was there, one could climb the spiral stairs outside the church tower to the very top and have a wonderful view over Copenhagen harbour and downtown.
Vor Frelser Kirke near the Orlogsmuseet
For me, climbing the spiral stairs outside the church tower was a breathtaking experience.