We describe the new, fast, high-precision microdensitometer SuperCOSMOS, Some aspects of hardware and software design that enable high-precision astrometry from photographic plates are explained. We show that the positioning repeatability of the measuring machine is less than 0.1 mu m standard error in either coordinate, and the absolute positional accuracy is about 0.15 mu m standard error. Furthermore, measurements of the same plate in different orientations show that the sampling errors are small (e.g. similar to 0.2 mu m, rising to similar to 1.0 mu m at the plate limit, for stellar images in a IIIaJ emulsion), thus allowing the extraction of relative positional information from Schmidt plates at accuracies less than 1 mu m. We demonstrate that SuperCOSMOS is capable of measuring the positions of bright stars (i.e. those more than similar to 4 mag above the plate limit) to a precision similar to 0.5 mu m with survey-grade photographic plates employing fine-grained emulsions.