The two are among the 33 miners rescued after a mine collapse in Chile last year.
Urzúa and Rojas were at the museum Sunday visiting an exhibit memorializing their two-month underground ordeal. "Against All Odds: Rescue at the Chilean Mine" has mementos on display including a small bible, a pair of dusty boots, a hard hat and even the famous capsule that carried the men out of the mine.
But visitors were even more amazed to see the miners themselves. "We... saw the sign that the capsule was here, so we wanted to make it a point of coming in here to see it, but we didn't expect to see the captain of the mining crew here. I expected to see a glow around him, very cool," said Leslie Cosenitne, who was visiting from North Carolina.
Urzúa, known for being the group's leader, is credited for aiding in the miners' rescue by keeping them calm underground. He was the last man to be rescued, and said he was born again the moment he was freed from the mine.
"I think God kept us alive for a reason and this experience is part of humanity, because not only did Chileans see it but the whole world saw it... and everyone wants to know something about our hope and how we thrived," Urzúa said in Spanish.
For 17 days, nobody knew whether the miners were dead or alive. The group rationed their food, uncertain when or if help would arrive.
According to a diagram of the San Jose mine on display at the exhibit, the men were more than 2,500 feet underground. That's the same distance as five Washington monuments stacked on top of each other.
The men say they simply did what they had to do to survive. "We followed orders and we respected everyone's opinion so that nobody would feel like they were in desperation," Rojas said in Spanish. "It was a terrible situation, but we controlled that and that's why we are where we are."
Rojas had three family members in the mine with him, and he's perhaps best-known for proposing to his girlfriend immediately after being freed. The two are now married.
Urzúa and Rojas will speak at a workshop on leadership this Tuesday, Oct. 11 (4:30-6 p.m.) at the Museum of Natural History's Baird Auditorium. Registration is required, but open to the public. You can register online here or by calling 202-633-3030.
Another special event Tuesday (7-9 p.m.) will include a premiere of the documentary film "Chilean Mine Rescue" and an appearance from the filmakers and a Smithsonian Channel exec. Tickets are free; you can register here.
Both men said they hope their experience will show the world that in a dark place, it's important to never stop searching for the light at the end of the tunnel -- whether literally or figuratively.