Many U.S. companies think their insurance policies cover lost revenue from the coronavirus outbreak. But that may be up to the courts to decide.

Corporations already have had claims rejected for payments under a popular type of coverage called business-interruption insurance, according to industry brokers and lawyers. In the rejections, insurers cited various terms and conditions, signaling that companies’ battle for recoveries will be slugged out almost policy by policy based on contractual language.

“There is no guesswork here: There will be insurance-coverage disputes,” said Kirk Pasich, an insurance-recovery attorney in Los Angeles.

Mr. Pasich represents several clients from the retail, construction and entertainment industries who are gearing up for legal action after their business-interruption claims were rejected. They filed those claims related to projects in China or Italy that got caught in quarantines or other government action that revoked their ability to operate, costing clients up to tens of millions of dollars, he said.

“There is so much money at stake and strong differences of opinions as to whether insurance applies,” he said.