Not only will Florida perform same-sex marriages, but there is no method for a legally married same-sex couple who has moved to Florida to obtain a divorce in Florida courts.
Same-sex marriage is not recognized in very many states, but evidence is showing that people are increasingly receptive to allowing same-sex marriage. With any marriage, things can go wrong, and divorce is sometimes necessary.
Unfortunately, those states that do not recognize same-sex marriage generally do not recognize same-sex divorce (this includes Florida). This is because granting a same-sex couple a divorce is basically a legal recognition that the couple was married in the first place — something these states aren’t ready to accept. If you are in one of these states, getting a divorce might require establishing residency in a state that recognizes marriage, meaning you’d have to move to that state for six months, a year, or even more.