A metacognitive radar switches between two modes of cognition—one mode to achieve a high-quality estimate of targets, and the other mode to hide its utility function (plan). To achieve high-quality estimates of targets, a cognitive radar performs a constrained utility maximization to adapt its sensing mode in response to a changing target environment. If an adversary can estimate the utility function of a cognitive radar, it can determine the radar's sensing strategy and mitigate the radar performance via electronic countermeasures (ECM). This article discusses a metacognitive radar that switches between two modes of cognition: achieving satisfactory estimates of a target while hiding its strategy from an adversary that detects cognition. The radar does so by transmitting purposefully designed suboptimal responses to spoof the adversary's Neyman–Pearson detector. We provide theoretical guarantees by ensuring that the Type-I error probability of the adversary's detector exceeds a predefined level for a specified tolerance on the radar's performance loss. We illustrate our cognition-masking scheme via numerical examples involving waveform adaptation and beam allocation. We show that small purposeful deviations from the optimal emission confuse the adversary by significant amounts, thereby masking the radar's cognition. Our approach uses ideas from revealed preference in microeconomics and adversarial inverse reinforcement learning. Our proposed algorithms provide a principled approach for system-level electronic counter-countermeasures to hide the radar's strategy from an adversary. We also provide performance bounds for our cognition-masking scheme when the adversary has misspecified measurements of the radar's response.