As of 1st of August 2014, you must use the blue EU health insurance card when travelling to an EU member state, Norway, Iceland, Switzerland or Liechtenstein. You still have to use the yellow health insurance card when visiting your GP in Denmark.
With the blue EU health insurance card you have the right to the same health insurance as the citizens of the country in which you are travelling.

The EU health insurance card is free of charge. It is valid for 5 years. You must order the card online. The card will be sent to you within 2 - 3 weeks. 

Udbetaling Danmark is responsible for processing applications for the blue EU health insurance card, as well as for issuing the card. If you have any questions regarding the blue EU health insurance card, you can find answers at borger.dk/EU-sygesikringskort or contact Udbetaling Danmark.