Friction between microscopic objects controls many macroscopic phenomena. For instance, the friction between microasperities determines the tribology of rough surfaces in contact and in relative motion. Additionally, the friction between microparticles is responsible for many aspects of the rheological response of granular media, ranging from microscale contacts at the single-particle level to macroscopic flow properties of sheared, dry granular systems and non-Brownian suspensions. We propose a new, precise, and robust method, based on lateral force microscopy, to measure the coefficient of friction between microspheres quantitatively and without complex data processing. We have successfully applied this method to the contact between silica spheres in liquid with and without a polymer coating.