There are day trips all around the Oresund which includes a normal circle of: Copenhagen to Malmo to Lund to Helsingborg by train and then ferry to Helsingor and train to the Louisiana museum and then back to Copenhagen; or in opposite direction.

There is a region pass ticket that allows for unlimited travel around the area for 2 days which states a requirement to cross by train in one direction and ferry in the other but which doesn't seem well monitored. It is a pretty good deal cost-wise given the roundtrip train ride across the bridge from CPH to Malmo by itself is at least 200 SEK absent the use of a discount purchase card (not available for sale at CPH).