This article proposes a design approach, based on the integral sliding mode control paradigm, devoted to give robustness to multiagent systems executing arbitrary distributed optimization and consensus protocols which do not take this feature into account. Robustness is understood as the capability of rejecting the effect of exogenous disturbances, parameter uncertainties, and uncertain couplings between the agents dynamics, by achieving the same emerging behavior as that corresponding to a reference multiagent system (MAS) designed to achieve a given coordination objective in the nominal case. The proposed approach yields a distributed state feedback which can seamlessly be integrated into existing distributed optimization and cooperative control protocols which are usually prone to disturbances and uncertainties corrupting the MAS dynamics. Nonsmooth Lyapunov analysis supports the claimed properties. Numerical simulations, showing how popular distributed optimization and consensus protocols can effectively be robustified are discussed.