After posting the information on Elizabeth's marriage, I was curious about the wording on the marriage certificate when it stated "by certificate". So here is what I have found out about Baptist marriages from the Archives Network Wales:
With the start of civil registration of marriage in the UK in 1837, Baptist marriages were legalised. A Baptist chapel could be used for marriage, if it was licensed for the purpose, and a Civil Registrar was present to complete the legal formalities, together with the minister who performed the marriage ceremony. In 1898, the requirement for the presence of a registar was changed. An authorised person, who need not be a minister, was allowed to act in place of the registar.