Soft matter research of natural organic and synthetic nanomaterials is an area in nanoscience and technology that has been growing particularly quickly in recent years. The materials under investigation are sensitive to high-energy electrons. Any structure characterization using electron microscopy thus requires special care. First, we illustrated this on naturally grown nanotubes observed by normal and cryogenic scanning electron microscopy. Second, we studied the ordering and orientation of the mesophase in template-grown nanotubes and nanorods containing discotic liquid crystals without and with doping, as desired. For these studies, we mainly used transmission electron diffraction and microscopy at low-dose conditions, high-efficiency image acquisition, and cryoprotection of the structures at liquid helium temperature. Additional analytical information was obtained by electron energy filtering observations.