This letter investigates Bayesian bounds on the mean-square error (MSE) applied to a data-aided carrier estimation problem. The presented bounds are derived from a covariance inequality principle: the so-calledWeiss andWeinstein family. These bounds are of utmost interest to find the fundamental MSE limits of an estimator, even for critical scenarios (low signal-to-noise ratio and/or low number of observations). In a data-aided carrier estimation problem, a closed-form expression of the Weiss–Weinstein bound (WWB) that is known to be the tightest bound of the Weiss and Weinstein family is given. A comparison with the maximum likelihood estimator and the other bounds of the Weiss and Weinstein family is given. The WWB is shown to be an efficient tool to approximate this estimator's MSE and to predict the well-known threshold effect.