Cooper, however, said comparisons to interracial marriage were irrelevant because through the millennia, the fundamental component of a couple's identity that was important was not race but gender.
"The limitation of marriage to a man and a woman is something that has been universal. It has been across history, across cultures, across society. The loathsome restrictions based on race are of an entirely different nature."
To illustrate their argument that Prop. 8 "causes pain and humiliation," lawyers for the plaintiffs called Zarillo and Katami as their first witnesses, before a break.
They will each be cross examined by the defense later in the day.
Some 100 supporters and opponents of the ban peacefully rallied outside the courthouse today.
Hollywood director Rob Reiner, an advocate of same-sex marriage rights, was in the gallery at the trial.
Walker, as well as lawyers for both sides, have all said they expect any ruling in the case to be appealed, opening the door to a battle in the U.S. Supreme Court.
In 2003, the Supreme Court struck down state laws against same-sex sodomy between consenting adults and ruled in 1996 that laws motivating anti-gay bias were unconstitutional.
Same-sex marriage is currently legal in only five states and the District of Columbia. Forty states have laws that define marriage as a union between a man and a woman.
Walker initially said he would allow for video recordings of the proceedings to be released daily on YouTube, but he was overruled today by the Supreme Court, which strictly prohibits cameras in most federal courtrooms.