For many applications it is important to measure the local work function of a surface with high lateral resolution. Low-energy electron microscopy is regularly employed to this end since it is, in principle, very well suited as it combines high resolution imaging with high sensitivity to local electrostatic potentials. For surfaces with areas of different work function, however, lateral electrostatic fields inevitably associated with work function discontinuities deflect the low-energy electrons and thereby cause artifacts near these discontinuities. We use ray-tracing simulations to show that these artifacts extend over hundreds of nanometers and cause an overestimation of the true work function difference near the discontinuity by a factor of 1.6 if the standard image analysis methods are used. We demonstrate on a mixed-terminated strontium titanate surface that comparing LEEM data with detailed ray-tracing simulations leads to much a more robust estimate of the work function difference..