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 degree orbital inclinations, thus limiting atmospheric studies to a small fraction of the total exoplanet population. We will introduce a new observational and analysis technique called planetary infrared excess (PIE) that relies on acquiring simultaneous, broad-wavelength spectra and resolving planetary infrared emission from the stellar spectrum. Next, we will demonstrate how this method could be used to characterize the atmospheres of non-transiting exoplanets, including rocky worlds orbiting the nearest M-dwarf stars (such as Proxima Centauri). Finally, we will detail the likely effectiveness of pending and planned space-based telescopes (such as JWST, Origins, and MIRECLE) for studying non-transiting exoplanets based on their current designs.