With the change in the marriage registration put forward by the GRO you now will not receive you marriage certificate in the service on the day of your wedding. Rather you sign a document in the service which we then pass to the GRO. They will then prepare and print your certificate for you. This means that your certificate will be ready in a few weeks following on from your wedding.
Currently (Jan 2022) Wiltshire has no on-line booking mechanism to receive your certificate, rather you need to phone 0300 0034570 to request and organise with the registrar to pick up your marriage certificate.