Nearly all low-mass stars are believed to exhibit subsurface convection, some level of magnetic dynamo activity, and radiative emission from chromospheric (T = 10,000 K) and coronal (T > 1 million K) layers above their photospheres. Linsky et al. (2020) highlighted the usefulness of comparing X-ray and H I Lyman alpha flux trends from cool stars as a way of constraining how these atmospheres are produced and maintained. Here, we seek to simulate chromospheric and coronal heating for a broad set of F, G, K, and M stars and investigate whether the observed trends in X-ray and Lyman alpha emission can be reproduced. We also produce a new conversion of the Sun’s observed time-variable X-ray emission (from the GOES 1-8 Angstrom band) into the lower-energy ROSAT/PSPC band more commonly used in studies of cool-star X-rays. Because we have not yet conclusively solved our Sun’s own chromospheric and coronal heating problems, we parameterize the rate of simulated energy deposition using known expressions for the maximum available Poynting flux and efficiencies of various proposed mechanisms (see, e.g., Cranmer & Winebarger 2019). A key input parameter turns out to be the driving velocity at the photospheric base of the coronal magnetic field lines. Straightforward extrapolation from mixing-length convection theory drastically underestimates the velocity required to explain the emission from M dwarfs. However, empirical trends from spectroscopically inferred microturbulence velocities seem to do a better job, and we will explore why this may be an important clue to the underlying physics. Lastly, we note that understanding the origins of X-ray and UV emission from cool stars will also help us better predict the present-day properties and long-term evolution of exoplanet atmospheres.