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We present a real-time fitter for 3D single-molecule localization microscopy using experimental point spread functions (PSFs) that achieves minimal uncertainty in 3D on any microscope and is compatible with any PSF engineering approach. We used this method to image cellular structures and attained unprecedented image quality for astigmatic PSFs. The fitter compensates for most optical aberrations and makes accurate 3D super-resolution microscopy broadly accessible, even on standard microscopes without dedicated 3D optics.