I do have an 1881 certificate of an 1846 Scottish birth but this will probably not be accepted by the purists as this was (A) produced in 1881 and (B) authenticated and signed rather than certified and signed but it was legal proof of the event
You could have 1001 post-hoc documents for legal proof of an event, but they can only contain information which was recorded in some form or other at the time when the event took place, for example church records or family bibles or newspaper announcements. Sometimes even the recollections of the people involved, in the absence of a written record. I'd have no problem accepting such a document.
If you choose to call it a certificate, that's fine, but it isn't especially helpful in the context of this particular query.
The fact remains that information about the parents of a couple getting married was not routinely collected in Scotland before 1855, when formal marriage certificates were introduced, and in England, Wales and Ireland the full details of the parents of a couple getting married are still not recorded at the time of marriage - only the names and occupations of the couple's fathers are on an English, Welsh or Irish marriage certificate.
