The resolution of helium ion scanning microscopes working in the secondary electron emission mode is theoretically estimated in the energy interval of E = 0.3-100 keV. The corresponding probe diameter improves with energy from 1.0 to 0.2 nm. A theoretical probe diameter of 0.25 nm can be obtained by use of a standard three-electrode objective lens of electrostatic microscopes. The most important ion-optical element of this device is the supertip ion source. The existing devices, however, need calibration of spatial resolution. Three elementary types of test objects are suggested: multilayer nano-structures of metal on insulator, metal-phthalocyanine crystals, and “noise-like” objects such as metal nano-particles on dielectric substrates. At low beam energies, a new type of contrast can be obtained in the mode of secondary electron registration with a resolution of about 1.1 nm.