The paper introduces ResMap, a method for determining local resolution in cryo-EM density maps. Unlike traditional methods such as Fourier shell correlation (FSC), which provide a single resolution value for the entire map, ResMap assesses resolution at each voxel, accounting for local variations. This is crucial because cryo-EM data often exhibit heterogeneity and image processing errors that affect resolution locally. ResMap is based on a statistical hypothesis test that determines whether a local sinusoid is statistically detectable above noise at each voxel. The test uses a likelihood ratio statistic to compare the fit of a local sinusoid model to a null model. The smallest wavelength (λ) at which the local sinusoid is detectable defines the local resolution at that voxel. This approach controls for false discovery rates (FDR) and accounts for dependencies between tests. The method uses steerable functions derived from second-order Hermite polynomials and Gaussian weighting functions. These functions allow for the modeling of any arbitrarily oriented local sinusoid in 3D. The algorithm iteratively tests each voxel, starting with a baseline wavelength and increasing it if the test fails, until a detectable sinusoid is found. ResMap was tested on simulated and experimental density maps, showing improved resolution estimates compared to traditional FSC methods. For example, in a ribosome reconstruction, ResMap-H2 estimates showed resolution variations between the 40S and 60S subunits, with the 40S subunit having lower resolution near the edges. In a virus reconstruction, ResMap-H2 indicated lower resolution in protruding domains, consistent with the original publication. In a GroEL reconstruction, ResMap-H2 showed resolution variations along an α-helix, with higher resolution in the central part. In an ATP synthase dimer reconstruction, ResMap-H2 indicated better resolution in the central dimer compared to neighboring structures. ResMap is more efficient than windowed FSC, requiring only a few minutes to process, whereas windowed FSC can take hours. Additionally, ResMap is less sensitive to the size of the user-defined window, making it more reliable for local resolution assessment. The method is implemented as a cross-platform software package with a graphical user interface. It is publicly accessible and can be applied to other fields by using different features, such as 2D Gaussian features for optical nanoscopy or rotated 2D arcs for radio telescopy. ResMap provides a statistically rigorous and practical method for assessing the local resolution of cryo-EM density maps, which is essential for evaluating the quality of these maps in studies of biological structures.The paper introduces ResMap, a method for determining local resolution in cryo-EM density maps. Unlike traditional methods such as Fourier shell correlation (FSC), which provide a single resolution value for the entire map, ResMap assesses resolution at each voxel, accounting for local variations. This is crucial because cryo-EM data often exhibit heterogeneity and image processing errors that affect resolution locally. ResMap is based on a statistical hypothesis test that determines whether a local sinusoid is statistically detectable above noise at each voxel. The test uses a likelihood ratio statistic to compare the fit of a local sinusoid model to a null model. The smallest wavelength (λ) at which the local sinusoid is detectable defines the local resolution at that voxel. This approach controls for false discovery rates (FDR) and accounts for dependencies between tests. The method uses steerable functions derived from second-order Hermite polynomials and Gaussian weighting functions. These functions allow for the modeling of any arbitrarily oriented local sinusoid in 3D. The algorithm iteratively tests each voxel, starting with a baseline wavelength and increasing it if the test fails, until a detectable sinusoid is found. ResMap was tested on simulated and experimental density maps, showing improved resolution estimates compared to traditional FSC methods. For example, in a ribosome reconstruction, ResMap-H2 estimates showed resolution variations between the 40S and 60S subunits, with the 40S subunit having lower resolution near the edges. In a virus reconstruction, ResMap-H2 indicated lower resolution in protruding domains, consistent with the original publication. In a GroEL reconstruction, ResMap-H2 showed resolution variations along an α-helix, with higher resolution in the central part. In an ATP synthase dimer reconstruction, ResMap-H2 indicated better resolution in the central dimer compared to neighboring structures. ResMap is more efficient than windowed FSC, requiring only a few minutes to process, whereas windowed FSC can take hours. Additionally, ResMap is less sensitive to the size of the user-defined window, making it more reliable for local resolution assessment. The method is implemented as a cross-platform software package with a graphical user interface. It is publicly accessible and can be applied to other fields by using different features, such as 2D Gaussian features for optical nanoscopy or rotated 2D arcs for radio telescopy. ResMap provides a statistically rigorous and practical method for assessing the local resolution of cryo-EM density maps, which is essential for evaluating the quality of these maps in studies of biological structures.