I believe that there is a service to bless an existing marriage when a couple becomes Orthodox. I don't know the specifics of it though.
Yes, there is the crowning, which is actually the second half of the Orthodox marriage service. Couples who enter the Orthodox Church usually have their marriages crowned, i.e. made sacramental.
My question however is more specific. In precise theological terms how does the Orthodox Church view non-Christian unions? I have read that the Moscow Patriarchate considers them valid. Is that the view of all who call themselves Eastern Orthodox?
I've seen only once a Muslim couple with children become Eastern Orthodox. Ironically, their married life before was not considered a sin such as fornication, nor was their children considered "born in sin". But like you said they were crowned right after their Baptisms and family's baptism.
It was more of a "recognition by the church" thing without condemnation of them "living in sin" or anything like that. I remember that a couple years later they had an anniversary including all the years when they were Muslims. I think it was treated as more that their years of marriage were "absorbed" (if that's a good word) into the church.
Two people that truly believed that they were married and lived in a faithful "marriage", who discovered Eastern Orthodox Christianity, found the errors of their ways - it would be kind of cold to say "Your kids are bastard children and your a bunch of evil fornicators". LOL They renounced Mohomet and his ways after all before the Baptism service.
They were treated as a long time married couple with children as any other member of the church before and after they were crowned.
Of course, I wasn't in on all the private details (or confession), but the atmosphere was very happy that they were there. I do recall the Priest addressing the church of this family (weeks before Baptism) as "Mr. * and his wife * and their family will be Baptized...". Of course, that could have been said tongue and cheek though.
That is a very interesting link though posted above.