Companies with a “plurality plus” standard for electing corporate board directors have a new warning to contemplate from the Delaware Supreme Court: Yes, you can ignore shareholder votes calling for a director’s ouster, but it will come at a price.

The case in question, Westland Police & Fire Retirement System v. Axcelis Technology, is the first to challenge a board’s decision not to accept a director’s resignation under a plurality-plus voting standard. That standard does not require directors to win an outright majority of votes to be elected, but it does require them to offer their resignation if ...