In this article, we report on the use of transmission electron microscopy (TEM) for the fabrication of high-performance textured amorphous/crystalline silicon (a-Si:H/c-Si) heterojunction (HJ) solar cells. Whereas classical thin-film characterization techniques allowed us to optimize the a-Si:H layer properties for flat HJ solar cells (open-circuit voltages (VOC) up to 710 mV and energy conversion efficiencies up to 19.1%), these techniques can not always be fully exploited on textured c-Si surfaces. Nevertheless, in this situation, TEM micrographs permit us to identify device performance limiting factors, such as, e.g., local epitaxy in pyramid valleys as the main source of our VOC-loss. Minimizing this local epitaxy by adjusting the amorphous Si based layers growth conditions and improving the c-Si surface morphology yields Si HJ solar cells with VOCs over 700 mV.