The application of scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) to the study of ceramic materials is demonstrated with analyses of SiC (6H) single crystals and polycrystalline ZnO both in air and under vacuum. In addition to observations of the surface structure of silicon carbide, mid-band-gap electronic states are identified, using STS under vacuum. Surfaces of the sintered ZnO were found to be terraced, having flat areas on the scale of tens of nanometers square, and typical step heights of 1 to 3 nm. The general conditions necessary to enable STM imaging of large-band-gap materials typical of most ceramics are discussed. In particular, the effects of doping to create mid-band-gap states and induce band bending due to space charging are illustrated in the analyses of SiC and ZnO.