We introduce a method of estimating the uncertainty of surface‐wave group velocity as measured by a single seismic station. However, because the method is designed for single‐station analysis, it does not consider possible phase delay induced by the earthquake source. The method uses the multiwavelet transform to decompose the seismogram into a series of complex valued, mutually orthogonal, time‐frequency coefficients, which are enveloped and normalized and used to pick the group velocity. The group velocities from each of the multiwavelet decompositions are then analyzed using standard statistical techniques to obtain the mean group velocity as well as, for example, standard deviation about the mean. We demonstrate our method on a synthetic data set as well as two ambient‐noise cross correlograms. An inversion of the estimated group velocities (as well as their corresponding uncertainties) yields a 1D shear‐wave velocity profile of a basin‐and‐range structure in the southwestern United States. This article includes links to MATLAB (see Data and Resources) scripts implementing the methods described herein.