To date, the ability for observers to reveal the composition or thermal structure of an exoplanet's atmosphere has rested on two techniques: high-contrast direct imaging and time-series observations of transiting exoplanets. The former is currently limited to characterizing young, massive objects while the latter requires near 90° orbital inclinations, thus limiting atmospheric studies to a small fraction of the total exoplanet population. Here we present an observational and analysis technique for studying the atmospheres of non-transiting exoplanets that relies on acquiring simultaneous, broad-wavelength spectra and resolving planetary infrared emission from the stellar spectrum. This method could provide an efficient means to study exoplanet atmospheric dynamics using sparsely sampled phase curve observations or a mechanism to search for signs of life on non-transiting exoplanets orbiting the nearest M-dwarf stars (such as Proxima Centauri). If shown to be effective with James Webb Space Telescope observations, the method of measuring planetary infrared excess would open up the large population of nearby, non-transiting exoplanets for atmospheric characterization.