In Europe each Municipality/Township has, within "County" offices, the "Electoral Bureau".
That is where the Electoral Certificates are issued.
In order to be eligible for one, you must be a certified resident of said Municipality or Township.
In order to be a Certified Resident, when you move into a new home you go and communicate your new address.
Simple as pie.
So you move house and arrive to your new address, you go to the Municipality and fill in a form, and Tadaa you are a certified resident.
From that moment on you "belong" in that Municipality and all official documentation is delivered to your official address.
Including your Electoral Certificate.
Without one, you cannot go and vote "just as well".
If you lose yours, you go to the Municipality and apply for another one, which will be issued to you right then and there even on election day - it's their job.
So if you guys in the New World have a problem, problem solved.
Just copy the Old World.