As we listen to speech, our ability to understand what was said requires us to retrieve and bind together individual word meanings into a coherent discourse representation. This so-called semantic unification is a fundamental cognitive skill, and its development relies on the integration of neural activity throughout widely distributed functional brain networks. In this proof-of-concept study, we examine, for the first time, how these functional brain networks develop in children. Twenty-six children (ages 4-17) listened to well-formed sentences and sentences containing a semantic violation, while EEG was recorded. Children with stronger vocabulary showed N400 effects that were more concentrated to centroparietal electrodes and greater EEG phase synchrony (phase lag index; PLI) between right centroparietal and bilateral frontocentral electrodes in the delta frequency band (1-3 Hz) 1.27-1.53 s after listening to well-formed sentences compared to sentences containing a semantic violation. These effects related specifically to individual differences in receptive vocabulary, perhaps pointing to greater recruitment of functional brain networks important for top-down semantic unification with development. Less skilled children showed greater delta phase synchrony for violation sentences 3.41-3.64 s after critical word onset. This later effect was partly driven by individual differences in nonverbal reasoning, perhaps pointing to non-verbal compensatory processing to extract meaning from speech in children with less developed vocabulary. We suggest that functional brain network communication, as measured by momentary changes in the phase synchrony of EEG oscillations, develops throughout the school years to support language comprehension in different ways depending on children's verbal and nonverbal skill levels.