She was ordered to pay more than $7,000 in attorneys' fees, which Willock waived.
The case has been cited as lawmakers in other states have proposed legislation exempting people from such lawsuits if doing business with same-sex couples violates their religious beliefs.
Arizona earlier this year passed such a law, but Republican Gov. Jan Brewer vetoed it under pressure and blistering criticism from major corporations and political leaders from both parties.
Similar religious-protection legislation has also been introduced around the country. And eight states, Alabama, Arizona, Kansas, Michigan, Montana, Oklahoma, South Carolina and Virginia, had asked the high court to hear the case so lawmakers would have guidance in considering such measures.
An Arizona-based group, Alliance Defending Freedom, defended the Albuquerque studio.
"Only unjust laws separate what people say from what they believe," said Alliance Defending Freedom Senior Counsel Jordan Lorence. "The First Amendment protects our freedom to speak or not speak on any issue without fear of punishment. We had hoped the U.S. Supreme Court would use this case to affirm this basic constitutional principle; however, the court will likely have several more opportunities to do just that in other cases of ours that are working their way through the court system."
The group said it is also defending cases like those of a Washington state florist and a Colorado cake artist who refused to do work for same-sex couples and a Kentucky T-shirt printer who declined to make shirts promoting a gay pride festival.
But Tobias Barrington Wolff, a University of Pennsylvania law professor representing the couple, said "no court in the United States has ever found that a business selling commercial services to the general public has a First Amendment right to turn away customers on a discriminatory basis.
"The New Mexico Supreme Court applied settled law when it rejected the company's argument in this case, and the Supreme Court of the United States was correct to deny certiorari review. The time had come for this case to be over, and we are very happy with the result."