The maximum depth of magnetization in the Earth’s crust is generally thought to coincide with the Curie temperature of magnetite (580 °C) and is commonly called the Curie depth. A popular approach to estimating the Curie depth is based on comparing the power-spectral density (PSD) of total-field magnetic anomaly data with theoretical expressions that describe the statistical properties of crustal magnetization and its depth distribution. However, the self-affine nature of magnetization (characterized by a power-law exponent in the PSD) renders this problem difficult in practice and several approximate methods have been devised to obtain estimates of the depth distribution and infer Curie depth variations using curve fitting of limited wavenumber ranges of biased PSD estimates. In most studies, however, errors are not carefully propagated through the estimation process and uncertainties in estimated parameters are not reported. In addition, robust spectral estimation techniques are required to map the spectral properties in space at the highest resolution possible and obtain Curie depth maps. Here we investigate the combined use of the robust multitaper spectral estimation technique with a Bayesian formalism to evaluate the recovery of the depth and statistical properties of the buried magnetized layer using a systematic analysis of synthetically generated data. Based on these tests, we come to the conclusion that most Curie depth estimates are not reliable, although it may be possible to obtain more reliable estimates through incorporation of prior information on one or all model parameters. Finally, we suggest that the spectral analysis of magnetic anomaly data may be better suitable to hotter settings, where shallow Curie depth estimates are more robust and in the oceans, where magnetization is likely to be uniform. These studies may also be more useful in retrieving the power-law exponent of magnetization as well as the depth to the top of the magnetized layer.