Based on the charging effect common to various kinds of electron microscopy, we have developed novel methods of determining "when" and "where" a probe starts to contact an electrically isolated surface. The touchdown of an electrically grounded probe leads to an acute change in the imaging contrast of the contacted surface, which also causes a rapid jump (ranging from a few to tens of picoamperes) of the grounding current. Thus, the detection of contact can be carried out in both qualitative and quantitative manners, providing a basis for establishing relevant standard procedures. In addition, we have achieved the spatial mapping of the contact point(s) using a specially designed lithographical pattern with two mutually vertical sets of parallel conductive lines. The precision of this mapping technique is simply determined by the pitch of parallel lines, which can be as small as the capability achievable in e-beam lithography. A possible "one-probe" version of the electrical characterization is also discussed with the same underlying principle, which may turn out to be indispensable for various studies and applications of nanostructures. Further development along this track is promising to realize an instrumentally simple version of "scanning electron spectroscopy" with various modes.