Prosodic cues in conversational speech aid listeners in discerning a message. We investigate whether acoustic cues in spoken dialogue can be used to identify the importance of individual words to the meaning of a conversation turn. Individuals who are Deaf and Hard of Hearing often rely on real-time captions in live meetings. Word error rate, a traditional metric for evaluating automatic speech recognition (ASR), fails to capture that some words are more important for a system to transcribe correctly than others. We present and evaluate neural architectures that use acoustic features for 3-class word importance prediction. Our model performs competitively against state-of-the-art text-based word-importance prediction models, and it demonstrates particular benefits when operating on imperfect ASR output.