Citizens of the European Union Member States plus Iceland, Liechtenstein, Norway, and Switzerland who travel within EU and EEA should have a European Health Insurance Card. The card ensures that holders get the same access to the public sector health care as nationals of the country they are visiting.
AS OF AUGUST 2014 THE REGULAR DANISH HEALTH CARD IS NO LONGER VALID FOR TRAVEL INSURANCE.
You can find an introduction to the rules concerning European Health Insurance Cards. Please note that third country citizens are not covered by the European Health Insurance Card in Denmark.
In Denmark, European Health Insurance Cards are only issued to citizens from the European Union Member States plus Iceland, Liechtenstein, and Norway, who are legally residing in Denmark.
It is always advisable for EU and EEA citizens to have a European Health Insurance Card when travelling within the EU and EEA. However, you are required to have a European Health Insurance Card with you when travelling in EU/EEA countries if you:
E101 is a posting certificate which you are required to have approved if your Danish employer sends you abroad to work temporarily (up to 12 months). An approved E101 obviates the need to join the social security system of the country to which you are sent. Your employer will usually apply for an E101 form for you. In Denmark E101 forms are issued by Sikringsstyrelsen.
Read more here.
The European Health Insurance Card gives you access to the same public sector health care as nationals of the country you are visiting during your temporary stay abroad.
European Health Insurance Cards are issued by municipal Citizens´ Services offices. A number of municipalities (including Aarhus) enable you to order a card online.
Read more how to apply for a card here.