We introduce voltage-contrast scanning electron microscopy (VC-SEM) for visual characterization of the electronic properties of single-walled carbon nanotubes. VC-SEM involves tuning the electronic band structure and imaging the potential profile along the length of the nanotube. The resultant secondary electron contrast allows to distinguish between metallic and semiconducting carbon nanotubes and to follow the switching of semiconducting nanotube devices, as confirmed by in situ electrical transport measurements. We demonstrate that high-density arrays of individual nanotube devices can be rapidly and simultaneously characterized. A leakage current model in combination with finite element simulations of the device electrostatics is presented in order to explain the observed contrast evolution of the nanotube and surface electrodes. This work serves to fill a void in electronic characterization of molecular device architectures.