That ruling followed a decision in December where Waddoups ruled Utah's ban on polygamous cohabitation was unconstitutional.
Utah Attorney General Sean Reyes has said previously that he planned to appeal the ruling and the decision Wednesday means the state could now proceed with an appeal.
Herbert said his counsel is still reviewing the ruling and he plans to discuss the state's course of action with Reyes, but he does not think it's a good idea to just drop the appeal.
"I think it's probably not good policy and practice for families to have that kind of situation," Herbert said. "That's my own provincial view with traditional marriage."
Herbert has similarly argued that he has an obligation to defend Utah's laws in court when it comes to the state's ban on same-sex marriage and the state's decision to appeal a judge's ruling striking down the ban to the appeals court and, more recently, to the U.S. Supreme Court.
In December, Waddoups ruled that the portion of Utah's anti-bigamy law making it a crime punishable by up to five years in prison for people cohabitating with unmarried partners violated the First and 14th amendments to the U.S. Constitution.
He let stand the portion of the law prohibiting someone from having more than one active marriage license.
In his ruling Wednesday, Waddoups found Utah County Attorney Jeff Buhman violated the Browns' constitutional rights when he oversaw a 2010 investigation into whether the Brown family was committing bigamy.
At the time the Browns lived in Lehi. They have since moved to Nevada. Buhman eventually decided not to file criminal charges, but Waddoups said the investigation stifled the Browns' rights to free speech, religion and equal protection. Waddoups ordered Utah to pay the Browns' attorney fees as a result of that finding.