For most of the earliest Scandinavian ballad texts to be written down, only the text was written down. But later melodies were often written down at the same time as the words. So similarly to ballad texts in English, for some there is no associated traditional melody, and for others there are one or more.

As for the ballad Unge Herr Svedendal, I don't think any melody is known. There are a few very similar Danish variants of this ballad (it's usually called Ungen Svejdal in Danish), and again, I don't think any melody is known for them either.

I've written a bit more on musical aspects of some of the Scandinavian ballads here:
http://balladspot.blogspot.co.uk/ with links to performances and so on.