We are on our way to Sonderborg as we write this. We were looking into how to get there from London and these are some of the ways we considered.
Travelling by Train
Sonderborg is well connected by train within Denmark. It is located at the end of a main line to Copenhagen with trains every 2 hours during the day. From Copenhagen, trains further afield to Sweden and beyond may also be taken. For trains further north in Denmark you need to change in Fredericia or Middelfart. Towards Germany you often need to change twice in Padborg and Flensburg.
Travelling by Bus
Travelling by Air
Sonderborg is graced by its own airport, which is around a 15 minute drive from the centre. The airport is, however, not very well connected: the only commercial flights available are to and from Copenhagen with Cimber Sterling. Therefore it is also convenient to investigate flights to nearby airports.
Airports in Jutland
Billund Airport is the closest international airport in Jutland. It is decently well connected internationally. As it is a Ryanair airport destination, cheap flights are also available. Not being on a train line, it is not well connected domestically. Regular buses are available to a number of destinations on the Jutland peninsula and beyond, though none directly to Sonderborg. One option is to take the bus to Kolding and train from there.
Airports Further Afield
Of course, the first obvious airport is Copenhagen Airport. Due to the very good connection between Sonderborg and Copenhagen Central trains station and then onwards to Copenhagen airport, this should be quite practical.
Another option is to go south to Germany. Hamburg airport is within reach and the train connections are easy enough. It should be possible to book a German taxi from Sonderborg to the airport for Euro 165 according to this site.