Same-sex couples who have fought so long for the right to marry are finding they also need to fight for the right to divorce.

It's a well-known fact that half of marriages will end in divorce. And with six states and the District of Columbia allowing same-sex marriage, it's no surprise that same-sex couples, too, would at times seek divorce.

But for some, like Jessica Port and Virginia Anne Cowan, who were married in California in 2008, divorce is hard to come by.

Maryland's highest court is hearing arguments today on the precedent-setting case to determine if same-sex marriages granted in other states can be dissolved in one where the marriage is not recognized.

"It's critically important for married same-sex couples in Maryland, that their marriages be recognized and respected," said Shannon Minter, legal director for the National Center for Lesbian Rights in San Francisco and one of the attorneys representing Port, told ABC News.

Granting divorce to same-sex couples has been an inconsistent practice within the state, lawyers involved in Friday's case said. Though they believe judges have granted about a half a dozen divorces for gay couples, their clients, Port and Cowan, and at least one other couple were recently denied that.

Minter emphasized that divorces "shouldn't depend on what judge you get."

Jana Singer, professor of law at the University of Maryland Francis King Carey School of Law who is not involved in the case, believes the reason the appeals court took this case "to resolve this inconsistency," she said. " When the Court of Appeals rules in this case there will be a consistent rule in Maryland about recognition of same-sex marriages validly contracted in other states."

The couple first requested a dissolution of their marriage and were denied in 2010 by a Maryland judge based on the fact that women's marriage is not legal in the state.

"The court finds that to recognize the alleged marriage would be contrary to the public policy of Maryland," Prince George's County Judge A. Michael Chapdelaine wrote in a two-page opinion.

Lawyers for the women argue that Maryland has long recognized marriages entered into in other states, even if the state itself has barred those marriages. For example, Maryland law bars an uncle and a niece from marrying, but the state will recognize that marriage if it legally occurred in another state.

Singer explains this saying the court applies what is known as the Comity law.

"Even where somebody couldn't get married in Maryland, if they validly got married somewhere else Maryland will recognize their marriage," she said.

She added that a provision within the law of Comity that states it is invalid if the ruling "would be contrary to receiving state strong public policy" could have been the basis for Chapdelain's decision.

The state also has no express prohibition banning the recognition of same-sex marriages from other states, lawyers argued before the seven-member appellate court Friday.

"There have been bills introduced in the Maryland," Minter said during the Friday hearing, referring to proposed Maryland stature that would not recognize a marriage when it was legally entered elsewhere.   "Legislature has repeatedly rejected those…"

"Is this marriage entitled to recognition?" Minter asked. "Yes, as long as the marriage was validly entered in another jurisdiction…its exactly as though the marriage has been entered in Maryland."

About a year and half ago Maryland's attorney general looked at the question of marriage validity. In his review of Maryland law he said in a formal opinion that the state should recognize out-of-state same-sex marriages that were valid where they were entered into.  The attorney general's ruling has been applied to state agencies, granting same-sex couples state benefits.

Maryland joins the ranks of Nebraska, Pennsylvania, Texas and Rhode Island where judges have denied gay couples divorces.

Responding to those cases, California and the District of Columbia recently passed laws allowing gay couples married in their jurisdictions to divorce there if their home state will not dissolve the marriage.

Minter said in an interview with ABC News that today's one-hour oral arguments went "very well."

"They asked a lot of questions, and they seemed to  really understand our arguments that this is just about Maryland applying its usual rule about out-of-state marriages," he said. "We hope they will rule on that basis."

It typically takes the court three to six months  after oral arguments to issue an opinion, but Minter is hopeful a decision will be made sooner.

"This couple has already waited nearly two years to get a divorce, and I think the court understands that," he said. "They will make every effort to rule as quickly as they can."

Regardless of the decision made by the high court, under a law passed this year Port and Cowan and other same-sex couples, will only have to wait until January 2013 for same-sex weddings, and by extension divorces, to be legal. Opponents of the new law, however, are seeking to overturn it in a potential voter referendum.

AP contributed to this report