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Electromagnetic pulses (EMP) present a serious threat for operation of high-power, high-energy laser facilities. Here, we present an efficient strategy for EMP mitigation with a resistive and inductive holder, which is supported by extended numerical simulations and validated in dedicated experiments at the kilojoule/picosecond (kJ/ps) Petawatt Aquitaine Laser (PETAL) facility. Moreover, we demonstrate how a combination of PETAL with the tens of kJ/ns Laser MegaJoule (LMJ) beams may suppress the EMP emission. This method opens another efficient way for the EMP control on high-power, high-energy laser facilities.