Even though I've lived my entire life close to or in Copenhagen, I still learn new things about the city. For example, I just learned yesterday, that there are tea rooms in Copenhagen and that it is really something to try!
A.C. Perch's Tea Room has been around since 2006, placed in central Copenhagen above the tea shop of the same name. The salon is in English colonial style, but in a more modern way than seen in the store below.
Sit down, order a pot of tea and enjoy it with a view over Kronprinsensgade or go for the high tea menu with a selection of small sandwiches, scones with clotted cream, lemon curd and marmelade plus cakes!!! With or without an additional glass of bubbles (210 kroner with, 190 kroner without). There are also some smaller menus (a pot of tea with sandwiches or a piece of cake, 135 kroner, or just a pot of tea (85 kroner, can be shared).
I know it's not particularly Danish, but it's still something!
It's a good idea to book a table in advance (and if you want to stay there longer than 1 1/2 hours, specify for how long in the text field on the reservation page): http://www.perchstearoom.dk/default.asp?page=reservation.asp
Forget about coffee, you're in a tea salon! :)
Opening hours: Monday-Friday, 11:30-17:30, Saturday, 11-17, closed on Sundays.
At Kronprinsensgade 5, KBH K.