Democratic Pennsylvania Gov. Josh Shapiro and Republican Virginia Gov. Glenn Youngkin — speaking at different times but delivering a similar message — on Monday were part of a bipartisan blast of criticism aimed at the organization that runs the power grid in a 13-state region.

The message: PJM Interconnection must reform, or states will drop out and use other arrangements to manage the flow of electricity.

“If we need to chart a new course … we will,” Mr. Shapiro — who filed a lawsuit against PJM earlier this year — told a crowd in Philadelphia at a daylong conference focused on the much-criticized PJM. Mr. Youngkin said if PJM doesn’t change, his state will “do what is needed” to protect its families.

PJM — the regional grid operator for all or part of 13 Mid-Atlantic states and the D

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