One very important thing to note about credit card use in Denmark is that it no longer is common to have your card's magnetic strip read and then sign a receipt.
All (at least almost all) terminals in stores and hotels and hand held terminals in restaurants and even taxis expect that the card has a chip and that you know your pin code.
As for public transportation you can buy tickets at train stations with a credit card, but not in buses. Though the bus driver has some change, don't expect the driver to be able to give change back for 100 kroner notes. If you plan on travelling by bus, get hold of some 20 kroner coins.
Bus tickets in Denmark are area and time limited, so you can't buy a return ticket. Only when travelling longer distances can you buy return tickets for trains (you have to travel across regional boundaries).