If you live in a state that bans same-sex marriages and you were married in another state (that does legally recognize those marriages), you more than likely can't get divorced in your home state because your state law doesn't recognize your relationship.
Courts in states that have a state version of the Federal Defense of Marriage Act prohibiting marriage of same-sex partners, will almost certainly deny you an ability to get divorced in their state. Additionally, you may not be able to get divorced in the state where you were married because that state may not have the power and/or authority to grant the divorce because they may not have jurisdiction over you, if you are a nonresident and can't meet the residency requirements of that state.
If the court in your state refuses to apply its own divorce statutes or the statutes of the state that issued the marriage certificate, a couple wanting a divorce could always ask the court for equitable relief. To establish a need for equitable relief, one or both partners will need to show the following:
- No other suitable legal remedy is available.
- Without a divorce, the couple will suffer real harm.
- No equitable defenses would prohibit the court from granting a divorce.
- The court has the discretion to grant the divorce based on equitable jurisdiction.