A considerable amount of image processing techniques known as inpainting techniques have been recently developed aiming to provide solutions for filling in missing or damaged regions in a digital image. Typical such techniques reconstruct a defined area by using information from its neighborhood, for example, by completing inside the missing region the isophote lines arriving at its boundaries. In this article, we show that inpainting techniques have considerable potential usefulness in microscopy imaging, even though experimenting and using them in this domain has been almost entirely neglected up until now. In this purpose, we experiment the "curvature-preserving" partial differential equations as a solution to inpainting regions in images collected by several optical and scanning probe microscopy techniques. The results achieved are presented along with a discussion on typical problematic scenarios of microscopy imaging for which this type of techniques can provide a viable solution.