There are daily flights to and from Copenhagen. Flying with Cimber Air, the ticket price ranges from 295DKK to over 1000DKK.
Train connections to and from most danish cities are available. DSB
If driving north on the E45 highway coming from Germany, route 8 is the fastest way to get to Sønderborg. If driving south on E45, route 41 is the fastest.
Sønderborg is located not very far from the Danish-German border. Just south of the border is the German town of Flensburg, which is popular amongst Danes going to Germany on a one-day trip, often to shop and to buy alcohol and chocolate, which is cheaper in Germany than in Denmark.