Since it’s launch in 2018, TESS has discovered more than 60 confirmed exoplanets. Among these, about a third are terrestrial and orbiting M- or K-dwarfs, which makes them prime candidates for follow up characterization studies with the James Webb Space Telescope (JWST). In this study, we construct a model grid of thermal emission spectra for 15 of these planets. These models vary by composition, surface pressure, and planetary Bond albedo. With these models constructed, we predict the observability of each with JWST by simulating observations using PandExo and Pandeia. Utilizing χ2 tests, we find that atmospheres on all of these planets except LHS 1815b and GJ 143c could be detected in less than 10 eclipses using JWST’s MIRI LRS instrument. Individual species such as SO2 can be detected in thin atmospheres on LHS 3844b and LP 791-18b as well as in thicker atmospheres for the other planets in less than 10 eclipses. Eclipse depths of thin atmospheres can readily be detected using MIRI’s photometric filters centered at wavelengths redder than 10 microns, and using relative photometry, atmospheres could be detected in less than 10 eclipses on LHS 3844b, LP 791-18b, GJ 1252b, and LTT3780b. Spectroscopy with MIRI LRS is more efficient than photometry, but photometry can provide an efficient means to flag terrestrial planets as cool as 650 K for future study. Dedicated observing programs to characterize these planets could provide answers concerning the formation and habitability of planets around M- and K-dwarfs.