Hello As in normal marriages they have 4 options, 1/ Neither wears an engagement ring, 2/ Both do, 3/ one does as in the "Bride", 4/ The other one does as the "Groom". As it is normal for the Bride to get a wedding ring and optional for the Groom, I would forgo the Engagement rings and both get Wedding rings Andy C.
It's the same as in all the marriages. Yes they wear engagement rings and new rings are presented at the time of the ceremony. Everything is the same.