When you travel in Europe (the European Union, European Economic Area and Switzerland), the European Health Insurance Card covers you in accordance with the modalities of each country that you visit.
However, conditions are quite often less advantageous than in Luxembourg. You will be responsible for all or part of the fees billed to you.
Outside the European Union, the CNS has set up agreements with certain countries such as Cape Verde, Tunisia, and Morocco, for reimbursements at the local price through the national health care organization of each country.
In countries not covered by a care agreement, you must pay the entire bill for all medical costs. Upon your return to Luxembourg, you will be able to request a reimbursement from CNS, based on the system in place in Luxembourg. Imagine the consequences if you have to have an emergency operation in the United States, where health care costs are much higher than in Luxembourg.
Coverage offered by Social Security for substantial health care costs incurred abroad often proves to be insufficient. If you do not have a travel-specific insurance you run a high risk of going into debt in cases involving evacuation or surgical intervention, because the costs of care abroad can reach several hundred thousand euros for more expensive destinations (e.g. The US), and will then be your responsibility, in whole or in part (in cases of partial reimbursement by the CNS or a supplementary health insurance).