In lensless digital holography, the comparatively low resolution of the CCD devices that are used to record the digital holograms has to date limited both the maximum linear dimensions of the measurement object and also the minimum possible stand-off distance between the object and the CCD detector. A signal-processing-based technique known as superresolution (SR) image reconstruction can provide an alternative approach that reduces these restrictions. We report on an SR image reconstruction technique that has been introduced by employing a camera with a "microscanning" function to capture SR digital holograms via multiple subpixel movements of the CCD sensor. A detailed description of the approach is given, along with experimental results, which are discussed and evaluated, showing the advantages of using this method. An approach using three-dimensional holographic contouring is also described that may be adopted as a strategy for benchmarking newly developed algorithms at any stage of the lensless digital holographic process.