In this paper we develop methods for evaluating uncertainties in the frequency response of a dynamical system based on finitely many input output data points. We extend the "Leave-out Sign-dominant Correlation Regions" (LSCR) algorithm to deliver confidence regions with a guaranteed probability for the frequency response at multiple frequencies, and we introduce a computationally efficient scheme that enables the confidence regions to be constructed frequency by frequency. Simulation examples illustrating the usefulness of the developed algorithm are provided. (C) 2015 Elsevier Ltd. All rights reserved.