From 1st of July it is allowed to enter Hungary without any restriction (no quarantine, no test) for every person, regardless of his/her nationality, who holds an EU digital COVID-certificate. Restrictions were lifted in case of flight travelers too. Persons vaccinated in Belgium can download the European certificate from the site of masante.belgique.be. It is possible to request the certificate by post at the following telephone numbers:
Flanders: 078/78.78.50
Wallonia: 071/31.34.93
Brussels Capital: 02/214.19.19
German Speaking Community: 0800 23.032.
Information on the conditions of travelling to Hungary (website of the Hungarian police)