In Frederiksberg you can park for free in most places for two hours. However, be aware that there is only 30 min parking on the Gl. Kongevej itself.
You must be digitally registered from the start of parking. Either buy a parking ticket or have a parking license. The first two hours are free. This applies to all weekdays between 07.00-24.00 and Saturdays between 07.00-17.00.