Using a point spread function (PSF) to localize a point-like object, such as a fluorescent molecule or microsphere, represents a common task in single molecule microscopy image data analysis. The localization may differ in purpose depending on the application or experiment, but a unifying theme is the importance of being able to closely recover the true location of the point-like object with high accuracy. We present two simulation studies, both relating to the performance of object localization via the maximum likelihood fitting of a PSF to the object's image. In the first study, we investigate the integration of the PSF over an image pixel, which represents a critical part of the localization algorithm. Specifically, we explore how the fineness of the integration affects how well a point source can be localized, and find the use of too coarse a step size to produce location estimates that are far from the true location, especially when the images are acquired at relatively low magnifications. We also propose a method for selecting an appropriate step size. In the second study, we investigate the suitability of the common practice of using a PSF to localize a microsphere, despite the mismatch between the microsphere’s image and the fitted PSF. Using criteria based on the standard errors of the mean and variance, we find the method suitable for microspheres up to 1 μm and 100 nm in diameter, when the localization is performed, respectively, with and without the simultaneous estimation of the width of the PSF.