The closest stars that harbour potentially habitable planets are cool M stars. Upcoming ground- and space-based telescopes will be able to search the atmosphere of such planets for a range of chemicals. To facilitate this search and to inform upcoming observations, we model the high-resolution reflection spectra of two of the closest potentially habitable exoplanets for a range of terrestrial atmospheres and surface pressures for active and inactive phases of their host stars for both oxic and anoxic conditions: Proxima b, the closest potentially habitable exoplanet, and Trappist-1e, one of the three Earth-sized planets orbiting in the habitable zone of Trappist-1. We find that atmospheric spectral features, including biosignatures like O2 in combination with a reduced gas like CH4 for oxic atmospheres, as well as climate indicators like CO2 and H2O for all atmospheres, show absorption features in the spectra of Proxima b and Trappist-1e models. However, for some features like oxygen, high-resolution observations will be critical to identify them in a planet's reflected flux. Thus, these two planets will be among the best targets for upcoming observations of potential Earth-like planets in reflected light with planned extremely large telescopes.