Under the Carriage of Goods by Sea Act (COGSA) the most recovered from the shipping line if they are “proven” negligent is $500 for each customary freight unit. Air carriers limit liability is $20 per kilogram. The carriers have multiple reasons for declining claims which would allow them not to have any liability at all. Some of them (but not limited to) are:

Act, neglect or default of the master, mariner, pilot or the servants of the carrier in the navigation or in the management of the ship.
Act of God.
Act of War.
Fire, unless caused by the actual fault of the carrier.
Perils, dangers and accidents of the sea or other navigable waters.
General average declared.