The Port of Copenhagen operates a parking lot at the Freeport Terminal (Tel. +45 35 46 11 09).
The price is 10 EUR per day.
There are plenty of parking lots in Copenhagen city center, which is not far from Langelinie Pier and the Freeport Terminal. You can buy a parking card valid for a week for DKK 610 (about $98); DKK 81 (about $13) per day after the first week.
For more information on car parking and a map of parking lots in Copenhagen, visit www.parking.dk.