They're gigantic: the largest ones weigh 500 tons each and stand 11 stories high - and they'll be outfitted with hoses and sophisticated air pumps to create buoyancy.
Here's what's supposed to happen: one by one, nine of them will be welded across the exposed side of the ship.
Sergio Girotto: They will be joined together like a big Lego, outside in the open.
Lesley Stahl: And they have to be precisely welded, correct?
Sergio Girotto: The space from one sponson to the other, it is less than two inches. So they must be fabricated with a very strict tolerance.
This row of hydraulic pulleys will tighten a string of 36 cables attached to the sponsons, slowly rolling the ship upright.
Then other steel boxes will be welded to the other side of the vessel and eventually, the hollow, air-filled sponsons will act like waterwings so the Costa Concordia can be floated and towed away.
Lesley Stahl: Has this ever been done before?
Sergio Girotto: No, no.
Lesley Stahl: This is brand new?
Sergio Girotto: The-- brand new technology, brand new methodology. To lift a vessel in this way, it is the first time ever.
And no one's 100 percent sure lifting a vessel this gigantic in one piece is going to work. It's the biggest passenger ship ever wrecked -- twice the size of the Titanic.
Just a year ago it was a 15-story floating palace - big enough to house a small town of 4,000 people. As this promotional video shows, it had 1,500 luxury cabins. Eighteen restaurants and bars, four swimming pools, five jacuzzis, and a casino.
The accident occurred this past January - ominously on the night of Friday the 13th. Nervous passengers crowded together as water gushed in. Sailing too close to shore, the ship had struck a huge boulder hidden just beneath the surface.
Lesley Stahl: You can see that it just tore the pipes apart.
Nick Sloane: Yeah the momentum of a large ship like this hitting that rock. She had no chance.
Lesley Stahl: Almost like a shark eating the belly of a whale or something, it just ate into that.
Nick Sloane: Yeah, it was a big rock, about 96 tons.
The wreck's an eyesore right off the beaches of tiny Giglio Island that has been overrun by an armada of support vessels and an army of welders, crane operators and marine engineers. Because of the angle of the ship, the workers have to take a four-day course in mountain climbing. Here they're working on the strong cables that are keeping the ship in place.
Much of the work is being done underwater by specially-trained salvage divers - 111 in all.
Ebano who's from Brazil is being geared up and safety checked by other divers on his team.
Nick Sloane: He's got communication for talking. He's got the air. He's got back-up air. He's got a camera and a light.
Everyone who goes in has a support team of at least five up on deck. Once suited up, Ebano is lowered down in a cage.
The day we were there the divers were ratcheting, tightening - measuring those massive steel cables that run under and around the ship to tie it down so it doesn't slide of the mountain peaks and sink.