Kommuneservice needs to certify if the parties meet the requirements to enter marriage according to Danish law. The municipality will, after the certification, issue and send you are marriage certificate.
Along with you foreign marriage certificate, you must provide a translation of the document to your local National Registry who will then register the marriage in the Civil Registration System.
NB! Be aware that when entering marriage abroad, there are different rules concerning names: Couples, who live in Denmark at the time of entering marriage abroad, will keep the names they had before the marriage. The surname of the spouse can only be obtained by virtue of a name certificate issued by The Danish State Administration (no charge).