Much recent psycho- and neuro-linguistic work has aimed to elucidate the mechanisms by which sentence meanings are composed by investigating the processing of semantic mismatch. One controversial case for theories of semantic composition is expressions such as the clown jumped for ten minutes, in which the aspectual properties of a punctual verb clash with those of a durative modifier. Such sentences have been proposed to involve a coercion operation which shifts the punctual meaning of the verb to an iterative one. However, processing studies addressing this hypothesis have yielded mixed results. In this study, we tested four hypotheses of how aspectual mismatch is resolved with self-paced reading and magnetoencephalography. Using a set of verbs normed for punctuality, we identified an immediate behavioral cost of mismatch. The neural correlates of this processing were found to match effects in midline prefrontal regions previously implicated in the resolution of complement coercion. We also identified earlier effects in right-lateral frontal and temporal sites. We suggest that of the representational hypotheses currently in the literature, these data are most consistent with an account where aspectual mismatch initially involves the composition of an anomalous meaning that is later repaired via coercion.