Of excellent value in the area surrounding København is a 24-hour rover ticket, which for DKK 130 (approximately £15 at current prices) gives travel on all trains, buses and metros in the area surrounding the capital. This includes travel to and from the airport, and out as far as Roskilde on the loco-hauled routes towards Kalundborg and Nykøbing. The child equivalent is available for DKK 65.
Quick two-step guide to purchasing them on the red DSB touchscreen ticket machines at stations:-
European Traction 