The paper introduces a novel method for defining and measuring local resolution in 3D density maps from electron cryo-microscopy (cryo-EM). The authors propose an algorithm, named ResMap, which uses local sinusoidal features to assess variable resolution across the density map. Unlike traditional Fourier shell correlation (FSC) methods, ResMap does not produce a single resolution value for the entire map but instead provides a local resolution map with a resolution assigned to each voxel. This approach addresses the limitations of FSC, such as its inability to account for local heterogeneity and image processing errors, and its sensitivity to the choice of window size in windowed FSC methods. ResMap is based on a likelihood-ratio hypothesis test that controls for false discoveries using a Benjamini-Yekutieli procedure. The method is evaluated on simulated and experimental density maps, showing consistent results with other resolution measures and providing insights into the resolution variations within and around particles. The software implementation of ResMap is publicly available, making it a valuable tool for researchers in cryo-EM and related fields.The paper introduces a novel method for defining and measuring local resolution in 3D density maps from electron cryo-microscopy (cryo-EM). The authors propose an algorithm, named ResMap, which uses local sinusoidal features to assess variable resolution across the density map. Unlike traditional Fourier shell correlation (FSC) methods, ResMap does not produce a single resolution value for the entire map but instead provides a local resolution map with a resolution assigned to each voxel. This approach addresses the limitations of FSC, such as its inability to account for local heterogeneity and image processing errors, and its sensitivity to the choice of window size in windowed FSC methods. ResMap is based on a likelihood-ratio hypothesis test that controls for false discoveries using a Benjamini-Yekutieli procedure. The method is evaluated on simulated and experimental density maps, showing consistent results with other resolution measures and providing insights into the resolution variations within and around particles. The software implementation of ResMap is publicly available, making it a valuable tool for researchers in cryo-EM and related fields.