"Married people who make a lot of money will pay more being married," Cowhey said. "But if you have one breadwinner and a stay-at-home spouse, you will probably less in taxes."
While there may be no way to get around the marriage penalty, there might be one-time planning opportunities to take advantage of, Cowhey explained.
For example, the issue of adoption credits.
Estate planners advise their clients who are not a child's biological parents to adopt them, known as a second parent adoption. This smoothes out any problems in the case of the death of the other parent, McClintock explained.
Read MoreRuling to impact gay couples' finances
Taxpayers are eligible for a $13,400 tax credit for adoption.
"But once you're married, you can't get it if you're adopting your spouse's child," said Cowhey. For that reason, Cowhey recommends that the non-biological parent do the adoption and claim the credit prior to marriage.
The Supreme Court's action marks the culmination of an unprecedented upheaval in public opinion and the nation's jurisprudence.
"The court now holds that same-sex couples may exercise the fundamental right to marry. No longer may this liberty be denied to them," Justice Anthony Kennedy wrote in the majority opinion. He was joined in the opinion by the court's liberal justices Ruth Bader Ginsburg, Stephen G. Breyer, Sonia Sotomayor and Elena Kagan.
All four of the court's most conservative members—Chief Justice John G. Roberts Jr. and justices Antonin Scalia, Clarence Thomas and Samuel A. Alito, Jr.—dissented and each wrote separate opinions.