The financial woes of one of the world’s biggest shipping lines have left as much as $14 billion worth of cargo stranded at sea, sending its owners scurrying to try to recover their goods and get them to customers, according to industry executives, brokers and cargo owners.

Since Hanjin Shipping Co. of South Korea filed for bankruptcy protection there last week, dozens of ships carrying more than half a million cargo containers have been denied access to ports around the world because of uncertainty about who would pay docking...