For in-situ measurements of the local electrical conductivity of well-defined crystal surfaces in ultra-high vacuum, we have developed two kinds of microscopic four-point probe methods. One involves a "four-tip STM prober," in which four independently driven tips of a scanning tunneling microscope (STM) are used for measurements of four-point probe conductivity. The probe spacing can be changed from 500 nm to 1 mm. The other method involves monolithic micro-four-point probes, fabricated on silicon chips, whose probe spacing is fixed around several mum. These probes are installed in scanning-electron-microscopy/electron-diffraction chambers, in which the structures of sample surfaces and probe positions are observed in situ. The probes can be positioned precisely on aimed areas on the sample with the aid of piezoactuators. By the use of these machines, the surface sensitivity in conductivity measurements has been greatly enhanced compared with the macroscopic four-point probe method. Then the conduction through the topmost atomic layers (surface-state conductivity) and the influence of atomic steps on conductivity can be directly measured.