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."
Biologists detail four new deep-sea 'killer sponges'
Pregnant Mila Kunis wins 'Best Villain' at MTV Movie Awards