Brilliant way to get to Copenhagen with a car. It's really good fun. Overnight ship with a great nightclub. They've always had really good bands playing whenever I've been. On the down side, it's quite a long drive from Esbjerg, and you still have to get a ferry to Sjælland.
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There's a car ferry or a suspension bridge to get to Sjælland. The bridge apparently only takes seven minutes, but I've only ever used the ferry, myself.