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To enhance frequency and active power control performance, this research proposes a decentralized robust optimal tuning approach for power grid frequency regulation support using energy storage systems (ESSs) as the primary source of grid-forming (GFM) converters. The proposed approach employs the robust Kharitonov theory to find a family of stabilizing sets of a proportional-integral (PI)-based supplementary controller, which is used in the outer control layer of the GFM control system. A family of stabilizing parameter sets is found in the presence of system uncertainties and disturbances that are common in power grid operation. Then, using a developed Bayesian optimization algorithm, an optimal set of parameters is determined among the mentioned family member sets. The proposed sophisticated combination of a robust control theorem and an optimization algorithm provides a promising solution for the robust and optimal tuning of control system parameters in ESS-based GFM converters. The efficacy of the proposed method is demonstrated via simulation and laboratory real-time experiment results for a given detailed case study.