The high-energy radiative output, from the X-ray to the ultraviolet, of exoplanet host stars drives photochemical reactions and mass loss in the upper regions of planetary atmospheres. In order to place constraints on the atmospheric properties of the three closest terrestrial exoplanets transiting M dwarfs, we observe the high-energy spectra of the host stars and in the X-ray with XMM-Newton and Chandra and in the ultraviolet with HST/COS and STIS. We combine these observations with estimates of extreme-ultraviolet flux, reconstructions of the lines, and stellar models at optical and infrared wavelengths to produce panchromatic spectra from 1 to 20 mu m for each star. While and do not possess primordial hydrogen-dominated atmospheres, we calculate that they are able to retain pure atmospheres if starting with 10, 15, and 50<!PCT!> of Earth's total budget, respectively, in the presence of their host stars' stellar wind. We use age--activity relationships to place lower limits of 2.2 and 6.6 Gyr on the ages of the host stars and Despite both and appearing inactive at optical wavelengths, we detect flares at ultraviolet and X-ray wavelengths for both stars. In particular exhibits two far-ultraviolet flares with absolute energies of 10 and 10 erg (equivalent durations of $4357 and $19724 s) occurring three hours apart. Based on the timing of the observations, we suggest that these high-energy flares are related and indicative of heightened flaring activity that lasts for a period of days, but our interpretations are limited by sparse time-sampling. Consistent high-energy monitoring is needed to determine the duration and extent of high-energy activity on individual M dwarfs and the population as a whole.