The X-ray and EUV emission of stars plays a key role in the loss and evolution of the atmospheres of their planets. The coronae of dwarf stars later than M6 appear to behave differently from those of earlier spectral types and are more X-ray dim and radio bright. Too faint to have been observed by the Extreme Ultraviolet Explorer, their EUV behavior is currently highly uncertain. We have devised a method to use the Chandra X-ray Observatory High Resolution Camera to provide a measure of EUV emission in the 50-170 Å range and applied it to the M6.5 dwarf LHS 248 in a pilot 10 ks exposure. Analysis with model spectra using simple, idealized coronal emission measure distributions inspired by the Chandra Low Energy Transmission Grating spectra of the M5.5 dwarf Proxima Cen and results from the literature finds the greatest consistency with a very shallow emission measure distribution slope, DEM ∝ T3/2 or shallower, in the range log T = 5.5-6.5, although this could be an artifact of systematic errors. Instead, cooler, more solar-like differential emission measures (DEMs) with a wide range of slopes were able to match the observations. Within the limitations of systematic errors, model spectra constrained by this method can provide accurate (within a factor of 2-4) synthesis and extrapolation of EUV spectra for wavelengths <400-500 Å. At longer wavelengths, models are uncertain by an order of magnitude or more and depend on the details of the emission measure distribution at temperatures log T < 5.5. The method is sensitive to the possible incompleteness of plasma radiative loss models in the 30-170 Å range for which reexamination would be warranted.
