N400 and P600 event-related potential (ERP) components have long been the object of study in psycholinguistics. Traditional accounts have associated N400 effects with semantic violations, and P600 effects with syntactic violations. However, this picture is complicated by P600 effects—without N400 effects—in response to animacy and thematic- role violations, as well as biphasic N400/P600 effects for conventional semantic violations. Building on explanations involving interplay of plausibility- driven and syntax-driven interpretations, we present a computational model that accounts for these complicating observations via a noisy channel modeling framework. Our model assumes early-stage sentence interpretations determined by noisy channel computation (influenced by plausibility), with these heuristic interpretations driving the N400 amplitude. The P600 then reflects a reconciliation with the true (syntax-driven) interpretation, impacted by the extent to which heuristic interpretations deviate from the true input. Running this model on original experimental stimuli, we successfully simulate N400 and P600 effects reported by eight studies in the literature that we examined. To our knowledge this is the first fully-specified computational formalization of plausibility/syntax interplay, the first implemented noisy channel model to carry out direct prediction of both N400 and P600 components.