Here is the travel planner
for travel from all stations in the Greater Copenhagen area to all stations in Southern Sweden, producing the calculations shown by Maxy (where DR byen - Lund cost DKK 109). Unfortunately it doesn't show the price, as Maxy also wrote.
The price from Copenhagen Main Station (H = Holovna) to Malmoe Central is DKK 89 - almost the same as the Swedish price, as Maxy also noticed. The price from Noerreport is the same as from Cph H. Price examples for other destinations in the region are listed here
On the Danish side tickets can be bought at stations (in the Seven-Eleven kiosks, the ticket sales on larger stations and in the DSB and SJ ticket machines). The only online sale I know of is at www.sj.se
. That site also know Noerreport, spelled in Swedish Nörreport.
The prices are relative high but at least you don't have to spend more money on connecting bus tickets
to get to the train. Why is that?
That is because the train tickets are valid for both train, metro and public buses in a certain area (zone) around the start point and the destination.
For instance a ticket from Copenhagen H to Malmoe include the zones F-L (covering the normal tarrif zones 1, 3 and 4 in Copenhagen (the central parts of the city all the way from the eastern border of zones 2 which is on the Frederiksberg metro station - Jagtvej - line. Refer to the zone map posted by Maxy where zone 1 is red) and zone A in Malmoe according to this map
I can't recommend the "metro-shortcut" between Noerreport and Copenhagen Airport.
The metro is an often crowded under-dimensioned service where much of the seating has been removed to make room for standing passengers.
A mini metro with only 3 wagons per train it is.
I would only use it on travels to the airport station if I was in a extreme hurry or if I was heading for/from a destination on the metro line (for instance Frederiksberg) and the use of the metro would save me for a change of transportation.
The travel time is only marginally longer on the regional train but the comfort level is much higher.
Furthermore the walking distance at the airport station is much shorter for the train than for the metro.
The travel time between Noerreport and Copenhagen Airport by metro is 17 minutes, by regional train, Øresundstog, it is 19 minutes.
The difference in total travel time can of course be more than 2 minutes due to the difference in waiting time: the metro depart every 2-6 minutes, the regional train every 10-20 minutes.