Perturbative unitarity is a powerful tool for inferring the range of validity of a given effective field theory. Here, we study such a bound in the parameter space of dimension-5 and dimension-6 effective operators that arise in a scenario of fermion compositeness. These operators are routinely used in experimental searches at the LHC to constraint contact and gauge interactions between ordinary Standard Model fermions and excited states of mass $M$. We derive the unitarity bound for the production process of an excited neutrino, then we implement such bound and compare it with the recent experimental exclusion curves for Run 2, the High-Luminosity and High-Energy configurations of the LHC. The results also applies to the searches where a generic single excited state is produced via dimension-6 contact interactions. The unitarity bound, so far overlooked in these effective models, is quite compelling and can serve as a guide for exploring the parameter space ($M,\Lambda$) in addition to the standard request $M \le \Lambda$.