Evaporation of liquids on substrates is important for many applications including lab-on-a-chip, especially when they are in droplets. Unlike on planar substrates, droplet evaporation on micropatterned substrates has been studied only recently and none so far on nanopatterns. Driven by the applicability of nanostructured surfaces to biomaterials and tissue engineering, we report on the evaporative process of sessile droplets of pure water and a protein solution on superhydrophobic surfaces of sharp-tip post structures in a submicrometer pitch (230 nm) and varying heights (100-500 nm). We find that the nanotopographical three-dimensionalities such as structural height and sidewall profile affect the surface superhydrophobicity in such a way that only tall and slender nanostructures provide the surface with great superhydrophobicity (a contact angle more than 170 degrees). The evaporation process was different between the pure water and the protein solution; unlike pure water, a significant contact-line spreading and pinning effect was observed in a droplet of a protein solution with an intermediate transition from a dewetting (Cassie) to a wetting (Wenzel) state. Enabled by well-defined nanostructures, our results highlight that the surface superhydrophobicity and the droplet evaporation are significantly affected by the three-dimensional nanometric topography and the surface fouling such as protein adsorption.