Several couples became joined in marriage on the New Year's Day.
Last year, the law had been approved and signed by Governor Martin O'Malley but its opponents had succeeded in gathering the sufficient number of signatures for a referendum in November. Voters then expressed their support for the law.
Brigitte Ronnett, 51, who married Lisa Walter, 51, hopes one day to see full federal recognition of same-sex marriage.
"I think it's a great sign when you see that popular opinion is now in favor of this," she told The Associated Press.