The ACT government argues its same-sex marriage laws should stand because they govern couples outside the federal definition of marriage as being between a man and a woman.
Ivan Hinton and Chris Teoh, who attended the court hearing, plan to marry on Saturday. Hinton said he knew of at least 12 other same-sex couples who planned to do the same.
Hinton said he hoped that the court would not order an injunction to prevent any marriage before the legality of the legislation was settled.
But when the hearing ended, the federal government did not apply for an injunction and the court issued no orders.
Australian federal law was amended in 2004 to specify that marriage can only be between a man and a woman. But it also specifically applied to heterosexual couples, and some lawyers argue that leaves states free to legislate for same-sex marriage.
Prime Minister Tony Abbott opposes gay marriage and his coalition last year thwarted two federal bills that would have allowed legal recognition of same-sex relationships.