Car rentals cost around DKr 1,185 per day for an economy manual vehicle. All major international car-rental agencies are represented in Copenhagen; most are at Copenhagen Airport or near Vesterport Station. The E20 highway, via bridges, connects Jutland with Funen, and goes on to Copenhagen. Farther north, from Århus (in Jutland) you can get direct auto-catamaran service to Kalundborg (on Zealand). From there, Route 23 leads to Roskilde, about 72 km (45 miles) east. Take Route 21 east and follow the signs to Copenhagen, another 40 km (25 miles).
The trip over the Øresund Bridge to Malmö, Sweden takes about 45 minutes, and the steep bridge toll stands at DKr 375 per car.
If you're only planning to sightsee in central Copenhagen, however, a car won't be convenient. Parking spaces are at a premium and, when available, are expensive. A maze of one-way streets and bicycle lanes make it even more complicated. If you're going to drive, choose a small car that's easy to parallel park.