We propose an approach for the characterization of scanning thermal microscopy (SThM) probe response using a sample with silicon dioxide steps. The chessboard-like sample provides a series of nine surfaces made of the same material, with identical roughness, but consisting of different thicknesses of silica layers standing on a single silicon wafer. The nine regions have different effective thermal conductivities, allowing calibration of SThM probes within a given set of surface conditions. A key benefit is the possibility of comparing the spatial resolution and the sensitivity to vertical inhomogeneities of the sample for different probes. A model is provided to determine the thermal contact area and contact thermal resistance from the experimental data. The results underline that ballistic heat conduction can be significant in crystalline substrates below the top thin films, especially for film thicknesses lower than 200 nm and effective thermal contact radius lower than 200 nm. They also highlight the sensitivity of SThM to ultrathin films, as well as the substrate below micrometric films under in-air conditions but not when in vacuum. This work advances quantitative nanometer-scale thermal metrology, where usual photothermal methods are more difficult to implement.