Germany is member of the Hague Convention (Hague convention abolishing the requirement of legalisation for foreign public documents, concluded October 5, 1961).
Denmark and Germany don't require according an agreement from 1936 any authentications from documents for the use in the other country. Danish documents of civil registries are not included in this agreement. For the use of the danish marriage certificate in Estonia, it is necessary the apostille by the danish authorities.
Danish civil registries don't require any authentication for documents issued in the EU