The paper describes a Bayesian approach to estimate the amplitude of a given signal embedded in complex zero-mean Gaussian noise with unknown covariance. By employing Jeffreys priors to unknown parameters, the posterior distribution is derived analytically. While the resulting estimates are merely reproductions of classical estimates, the Bayesian approach offers an enhanced ability to predict the quality of estimates conditioned on the measured data. This ability is further highlighted by simulations using finite training sets.