Resting-state functional connectivity (fc) has become a powerful tool for studying brain organization and development. Yet reliable analysis of fc patterns in individual subjects, which is crucial for clinical care and the study of brain-behavior relationships, is difficult due to high noise levels, short scan durations, and small sample sizes. Methods that pool information across subjects to inform estimation of subject-level effects (e.g., Bayesian approaches) have been shown to enhance subject-level fc reliability but remain underutilized. Fully Bayesian approaches are computationally demanding, while empirical Bayesian approaches typically require repeated measures to estimate variance components in the model. Here, we propose a novel fc measurement error model that avoids the need for repeated measures by describing the different sources of variance and error. We use this model to perform empirical Bayes shrinkage of subject-level fc towards the group mean, conduct reliability studies to validate and compare the resulting shrinkage estimates with those from traditional approaches, and apply the model to a study of autism to illustrate the clinical utility of the approach.