WASHINGTON—U.S. securities regulators have twice this week penalized firms for allegedly trying to silence whistleblowers, escalating a crackdown on severance arrangements seen as discouraging employees from reporting wrongdoing.

The settlements announced Tuesday by the Securities and Exchange Commission with an Oklahoma City energy company and Monday with a Virginia advertising firm follow five similar cases over the past two years against companies accused of illegally imposing “restrictive agreements” on departing employees—agreements...