Travel insurance for Hungary is worth arranging before you arrive, whether you fly into Budapest or come overland into Keleti Railway Station, the city's main international rail gateway. Hungary is a straightforward and popular destination in central Europe, and for many visitors the health-cover question comes down to what their European health card does and does not cover. The short answer is that a card helps, but it is not a substitute for travel insurance.
What the EHIC and GHIC cover
Hungary is in the European Union, so visitors from the EU with a European Health Insurance Card, and UK visitors with a Global Health Insurance Card, can use it to access state healthcare in Hungary. The important limit is that these cards only cover urgent or medically necessary treatment at public facilities, at the same cost a Hungarian resident would pay. They do not cover non-urgent care, treatment in private clinics, or, crucially, medical repatriation back to your home country, which can be the largest cost of all.
Why insurance still matters
For everyone else, and for anyone whose card does not stretch to cover their needs, travel insurance is recommended rather than mandatory. A policy fills the gaps the health card leaves: repatriation, private treatment with shorter waits and more specialists, cover for stolen belongings, and trip cancellation. If you travel from outside Europe, insurance is the primary protection, since the EHIC and GHIC schemes do not apply to you at all. Read the medical limit, the repatriation limit, and the exclusions before you rely on the policy.
Choosing a policy
Carry both if you have them: use the EHIC or GHIC for state care and a travel policy for everything else. If you are travelling around several European countries, confirm the policy covers each one. Subscription-style cover such as SafetyWing suits long or multi-country trips, while a fixed per-trip policy is usually better value for a single visit. Buy the cover before you leave home, because most insurers will not sell or honour a policy once your trip has already started, and keep both the card and the policy details somewhere easy to reach.