The Blue EU Insurance Card
This card ensures that, should you have a health emergency while visiting one of the EU countries (as well as Norway, Iceland, Liechtenstein - EEA, or Switzerland), you will be entitled to the same treatment as nationals of the country you are travelling in. Now, that may not necessarily mean that treatment will be free, unless the citizens of the country you are visiting receive treatment for free. Thus, to avoid unexpected medical expenses, you should be sure to take out travel insurance before you go on holiday, to ensure you can get the help you need, without taking a financial hit.
Ordering the card
If you, as an international, are here on a family reunification visa, you are eligible for the EU insurance card. You will need to go to Citizen Service (Borgerservice) on Odinsgade to order your card in person. Your Danish spouse will be able to order theirs online, but they cannot order for you.
For other internationals here on other visas, visit the European Commission's site for information on eligibility. You can also find information about the blue card here.
As of August 1st, your yellow Danish health insurance card will no longer cover you, should you have need of medical treatment outside of Denmark and its territories. If you haven't already, order your blue card now, to ensure you have it in time for any travel you have planned after August 1st.
It can take up to three weeks to get your card delivered, so be sure to order it now, rather than waiting until closer to your travel date. It's quick, easy, and painless.