Costa Crociere, an Italian unit of Miami-based Carnival Corp., invited 10 of the world’s largest salvage companies to bid on the massive removal project. Six companies or consortiums turned in plans – including Resolve and Titan Salvage.

The $300 million job went to Titan Salvage and its Italian partner, marine contractor Micoperi. In late May, they unveiled their plan to float the ship intact in a complicated, months-long operation.

Work has already begun and is continuing 24 hours a day. Crews have cut off some exterior parts of the ship and are working to remove the rock from the port side of the ship. Inspections are to continue until the end of the month.

Over the next six months, the wreck will be stabilized and supported with an undersea platform. To help roll the ship upright, workers will attach watertight boxes to the side that is out of the sea and fill those with water. Using cranes, crews will pull the ship upright and then refloat it by filling the same watertight boxes — plus another set on the other side — with air.

Refloating is expected to happen by Jan. 15, and the ship should be towed to a port by the end of January if all goes as planned.

While Titan is not allowed to say anything about the job beyond what has already been approved by Costa, some of the company’s previous projects hint at their expertise.

In 2007, the company won the contract for a project near Coos Bay, Ore., to remove the New Carissa, a wrecked freighter that had been stuck offshore for eight years. The job was considered difficult if not impossible because of rough sea conditions, said Titan’s senior salvage master, Shelby Harris.

But the company floated out two jack-up barges that stood above the water and fashioned a self-propelled cable car to shuttle workers from the mainland without subjecting them to the dangerous surf. After on-site work started in 2008, the job took less than four months.

Titan has earned a reputation for working with difficult wrecks, Harris said.

“Wreck removal is the fun stuff,” said Harris, who oversaw the New Carissa project. “You can plan it and you can be creative and you can build things.”

The company, with about 50 employees worldwide, has worked on more than 400 wreck removal and salvage projects over the years.

Todd Busch, a Crowley Maritime senior vice president who oversees Titan Salvage, said the unit might handle 7 to 8 projects in a light year or 15-20 when things get busy.

“This year, we’ve done 11 so far,” he said.

Jobs can be as simple as getting a large luxury yacht that has run aground back afloat or as complex as refloating a container ship piled with cargo. The APL Panama job in Ensenada, Mexico required tugboats, barges, a dredge, cranes, a helicopter, pullers and 20 trucks full of gear back in 2006.

Titan was awarded that job under a Lloyd’s Open Form contract, which means they had to pay all the costs of the job up front and get reimbursed after the fact. Busch said that depending on the type of contract used, a salvage company can spend tens of millions of dollars before getting any cash back.

Other agreements might be set at a fixed rate, but if unexpected costs emerge, the company could lose money.

And sometimes there is no guarantee of payment for work, such as when a company pursues a job on speculation. It can cost hundreds of thousands of dollars just to craft a proposal, Busch said.