A coherent X-ray scattering method for investigating the formation of the contact region between two solid surfaces is presented. Diffraction of X-rays from two crossed cylindrical quartz surfaces, coated with Cr and TiO(2), revealed a total contact area of 90 +/- 10 microm. In the so-called Hertz model for two surfaces in non-adhesive contact, this value is directly related to the displacement of the surfaces and the applied external force. Values of 40 +/- 3 nm for the displacement and 24 +/- 3 mN for the force are found. The method is also useful for studying liquids in confinement.