Colorado only allows civil unions. Mullins and Craig were married in Massachusetts, and planned to celebrate in Colorado.
The American Civil Liberties Union initiated the process on behalf of the couple last year.
The bakery owner faces up to a year in prison if the court rules against him and he continues to refuse to make wedding cakes for gay couples.
Mullins, 28, and Craig, 33, filed the discrimination complaint against Jack Phillips after visiting his business in suburban Denver in the summer of 2012. After a few minutes looking at pictures of different cakes, the couple said Phillips told them he wouldn't make one for them when he found out it was to celebrate their wedding in Colorado after they got married in Massachusetts. Phillips has said making a wedding cake for gay couples would violate his Christian religious beliefs, according to the complaint.
Phillips' attorney, Nicolle Martin, has said the case is about religious conscience and that one person's beliefs shouldn't be held above someone else's.
Colorado does not allow gay marriage, only civil unions. Colorado's civil union law, which passed earlier this year, does not provide religious protections for businesses despite the urging of Republican lawmakers. Democrats argued that such a provision would give businesses cover to discriminate.
A case similar to Colorado's is pending in Washington state, where a florist is accused of refusing service for a same-sex wedding.