Past research has sought to elucidate how speakers and addressees establish common ground in conversation, yet few studies have focused on how visual cues such as co‐speech gestures contribute to this process. Likewise, the effect of cognitive constraints on multimodal grounding remains to be established. This study addresses the relationship between the verbal and gestural modalities during grounding in referential communication. We report data from a collaborative task where repeated references were elicited, and a time constraint was imposed to increase cognitive load. Our results reveal no differential effects of repetition or cognitive load on the semantic‐based gesture rate, suggesting that representational gestures and speech are closely coordinated during grounding. However, gestures and speech differed in their execution, especially under time pressure. We argue that speech and gesture are two complementary streams that might be planned in conjunction but that unfold independently in later stages of language production, with speakers emphasizing the form of their gestures, but not of their words, to better meet the goals of the collaborative task.