That is a question of process, not substance, so the libertarian position would likely be neutral on that particular question, in a sense. I say in a sense, because the broader libertarian position on same-sex "marriage" would be that neither judges nor voters should decide, because, for the most part, government should not decide who can marry; it should be left to individuals/churches/etc. (Not arguing for that position, just speculating what it would be)
Welcome to the Constitution.
As to the process of getting judges to declare who can and cannot be married, the greatest damage that has been done to the fabric of this nation has been accomplished by judges. The solons who handed down the Dredd Scott decision all but started the Civil War. And the judges who handed down the Roe v. Wade decision started the culture wars.
If I were a libertarian, I would think thrice before going to the Supreme Court to accomplish cultural objectives which have been lost in the Court of Public Opinion.
Libertarians are not neutral, they are for homosexualizing the military and for homosexual “marriage”.
The libertarians exist to end/defeat political opposition to those positions, and to support/promote politics that supports those positions.