During the event, one of the miners, Claudio Yanez, got down on his knees and asked his girlfriend to marry him on her birthday.
The crowd cheered when she accepted his proposal.
Others are renewing their vows or planning church weddings years after being married in civil ceremonies.
The party, thrown by a Chilean mining millionaire, was the first public reunion for the miners since their dramatic rescue last week.
The party took place at Caldera's cultural centre, not far from Copiapo and the San Jose mine, to a crowd of 300 people.