During court sessions, between 9:30 a.m. and 11:30 a.m. on Mondays and Fridays, marriage ceremonies may be performed by the judge assigned to Session One, by appointment, upon presentation to the judge of a valid marriage license together with evidence of payment to the Clerk of Court of the amount listed in Schedule C of these local rules. The Clerk of Court shall provide a certificate of marriage to be signed by the judge following the performance of the marriage ceremony and furnished to the licensees. The certificate attached to the marriage license shall be signed by the judge and transmitted by the Clerk of Court to the Cuyahoga County Probate Court within thirty (30) days. The Clerk of Court shall keep a record of marriages performed by each judge and of the fees received.