3D single-molecule localization microscopy relies on fitting the shape of point-spread-functions (PSFs) recorded on a wide-field detector. However, optical aberrations distort those shapes, which compromises the accuracy and precision of single-molecule localization microscopy. Here, we employ a computational phase retrieval based on a vectorial PSF model to quantify the spatial variance of optical aberrations in a two-channel ultrawide-field single-molecule localization microscope. The use of a spatially variant PSF model enables accurate and precise emitter localization in x-, y- and z-directions throughout the entire field of view.