We consider an integrate-and-fire element subject to randomly perturbed synaptic input and an electrically coupled ensemble of such elements. The latter is interpreted as either a model of electrically coupled population of neurons or a multicompartment model of a dendrite. Random fluctuations blur the input signal and cause false responses in the system dynamics. For instance, under the influence of noise, the system may respond with an action potential to a subthreshold stimulus. We show that the responses of the elements within the network are more reliable than the responses of the same elements in isolation. Specifically, we show that the variances of the stochastic processes generated by the coupled model can be made arbitrarily small (i.e., the network responses can be made arbitrarily accurate) by increasing the number of elements in the network and the strength of electrical coupling. Our results suggest that the organization of cells in electrically coupled groups on the network level, or the dendritic morphology on the cellular level, may be involved in the filtering noise and therefore may play an important role in the information processing mechanisms operating on the network or cellular level respectively.