Ask employers how they’re doing on sexual harassment in the workplace and most will say pretty well. Employees have a different take.

Nearly 70 percent of leaders “strongly agree” that their workplace “does not tolerate harassment.” Fewer than half of workers outside of leadership roles say the same, finds a survey of 1,000 U.S. working adults. One in four said they saw or heard of an incident in the last year.

“There is a disconnect,” said Shahed Larson, a partner at the Brunswick Group, the public relations firm that fielded the survey.

#MeToo brought unprecedented awareness to the pervasiveness of...