The U.S. Supreme Court heard oral arguments March 25 about how to clear the muddy waters on whether injured sailors can sue shipowners for punitive damages when the accident involves claims that the ship was unseaworthy. Ship owner The Dutra Group asked the justices to overturn a federal appeals court’s decision allowing those damages in favor of a worker, whose hand was badly injured in an accident involving a broken hatch.

The high court previously ruled in 2009 that punitive damages are an option if an employer doesn’t provide medical care and wages to an injured sailor.

Now attorneys for...