Woods, the world's top-ranked player, and O'Meara were given a tour of the carrier Wednesday, signed autographs and put on a demonstration -- hitting some drives into the gulf to the cheers of the 6,000-member crew, officials said.
The two golfers flew in from the United Arab Emirates, where they are playing in the Dubai Desert Classic, a European tour event.
They were flown to the carrier on military aircraft for a visit of about an hour.
Woods said the visit was one of the "most awe-inspiring" of his life.
"I wanted to come out here because I was raised in the military, with my father being in the Army, and I understand the sacrifices he made for our country," Woods told the crew.
"And I understand all the sacrifices you are making for our country, and I want to honor that."
"We travel around a lot playing golf, but we can only do that because of what you all are doing for us," O'Meara told the crew. "We don't take that for granted."