Cryo-EM now commonly generates close-to-atomic resolution as well as intermediate resolution maps from macromolecules observed in isolation and in situ. Interpreting these maps remains a challenging task owing to poor signal in the highest resolution shells and the necessity to select a threshold for density analysis. In order to facilitate this process, a statistical framework for the generation of confidence maps by multiple hypothesis testing and false discovery rate (FDR) control has been developed. In this way, three-dimensional confidence maps contain signal separated from background noise in the form of local detection rates of EM density values. It is demonstrated that confidence maps and FDR-based thresholding can be used for the interpretation of near-atomic resolution single-particle structures as well as lower resolution maps determined by subtomogram averaging. Confidence maps represent a conservative way of interpreting molecular structures owing to minimized noise. At the same time they provide a detection error with respect to background noise, which is associated with the density and is particularly beneficial for the interpretation of weaker cryo-EM densities in cases of conformational flexibility and lower occupancy of bound molecules and ions in the structure.