Create a custom save button. Add a validation on this condition by retrieving a Registratie object from the database with the same values, e.g.
//Registratie [id != $Registratie] [Date = $Registratie/Date] [Registratie_Account = $Registratie/Registratie_Account] [Registratie_Event = $Registratie/Registratie_Event]
If such a registration exists, present the user with an error. Otherwise, commit the object.