Health and travel insurances are accepted in medical establishments in Romania, provided payment is confirmed first by the foreign insurance company.
EU citizens can get a European health insurance card (see details regarding EHIC here). The EHIC isn’t a substitute for medical and travel insurance, but it entitles you to state provided medical treatment that may become necessary during your trip. Any treatment provided is on the same terms as Romanian nationals.
You can purchase international travel insurance to arrive to Romania from your point of departure. Medical insurance companies in Romania sell health insurance packages for the duration of the stay within the territory of the Romanian State. For further info go to the website of the Romanian National Health Insurance House (see details here).
Before departure, check the vaccines and medicines list for Romania (see the CDC info for details) and visit your doctor (ideally, 4-6 weeks) before your trip to get vaccines or medicines you may need.
In Romania, as in any other EU country, if you need emergency medical assistance during your trip, dial 112 on your phone and ask for an ambulance. If you are referred to a medical facility for treatment you should contact your insurance/medical assistance company immediately.