Originally Posted by Aviatrix
Danes are used to cross-border visitors (especially from Germany) spending their own currency. (I grew up in Northern Germany, not far from the Danish border)
Don't forget about the Swedes, Malmo (the third largest Swedish city) is only 30 mins away by train, or across the bridge by car from Copenhagen.
I don't know anybody in southern Sweden (in county Skane) who doesn't go to Denmark to purchase alcohol.
At the ferry terminals or the railway stations (typical places where visiting Swedes end up) you can most likely pay with Swedish crowns but you get really bad exchange rate, so the best thing to do is to pay with the local currency.