We study whether a planner can robustly implement a state-contingent social choice function when (i) agents must incur a cost to learn the state and (ii) the planner faces uncertainty regarding agents' preferences over outcomes, information costs, and beliefs and higher-order beliefs about one another's payoffs. We propose mechanisms that can approximately implement any desired social choice function when the perturbations concerning agents' payoffs have small ex ante probability. The mechanism is also robust to trembles in agents' strategies and when agents receive noisy information about the state.