We consider the problem of safe control in discrete autonomous agents that use learned components for imperfect perception (or more generally, state estimation) from high-dimensional observations. We propose a shield construction that provides run-time safety guarantees  under perception errors by restricting the actions available to an agent, modeled as a Markov decision process, as a function of the state estimates. Our construction uses conformal prediction for the perception component, which guarantees that for each observation, the predicted set of estimates includes the actual state with a user-specified probability. The shield allows an action only if it is allowed for all the estimates in the predicted set, resulting in local safety. We also articulate and prove a global safety property of existing shield constructions for perfect-perception agents bounding the probability of reaching unsafe states if the agent always chooses actions prescribed by the shield. We illustrate our approach with a case-study of an experimental autonomous system that guides airplanes on taxiways using high-dimensional perception DNNs.