This letter devises a physics-informed neural hierarchical control for uncertain networked microgrids (NMs) to provide certificated safe and stable control of NMs undergoing disturbances and uncertain perturbations. The main contributions include 1) a learning-based hierarchical control framework for inverter-based resources (IBRs) in NMs under unprecedented uncertainties of renewable energies; 2) a robust control Lyapunov barrier function (rCLBF) to provide provable safety and stability guarantees under uncertain scenarios; 3) an rCLBF-based, physics-informed learning scheme to simultaneously discover the certificates and control policy with explicit safety, stability, and robustness guarantees, enabling certified generalization beyond nominal operating scenarios. The efficacy of the rCLBF-based neural hierarchical control is thoroughly validated in different NMs cases.