This paper provides detailed descriptions of the X-ray emission from supernova remnants (SNRs) evolving in warm, low-density, nonthermal pressureÈdominated regions K, n \ 0.001 cm~3, (T 0 \ 104 or 7200 K cm~3). Nonequilibrium ionization hydrocode simulations are used to predict the P nt \ 1800 high-resolution spectra, and keV ROSAT PSPC count rates, spatial appearance, color temperatures, 1 4 3 4 and ratios of O VII to O VIII emission-line Ñuxes as a function of time. If undisturbed, the remnants are quite long lived, surviving for D1.2 ] 107 to D1.6 ] 107 yr. During their brief energy-conserving phases, the hot, highly pressurized gas behind their shock fronts copiously emits X-rays. Thus, their keV 1 4 surface brightnesses are thousands of ROSAT PSPC counts s~1 arcmin~2 and the remnants appear strongly edge brightened. The onset of the radiative phase heralds the end of the extreme X-ray luminosities but not the end of the X-ray emission. After the cool shell forms behind the shock front, the hot SNR bubble slowly radiates away the remaining energy, with a diminutive fraction released in the form of X-rays. Thus, the keV surface brightnesses are tens to hundreds of ROSAT PSPC counts s~1 1 4 arcmin~2 and the remnants appear "" centrally Ðlled.ÏÏ The hot plasma within the remnant bubbles is always out of collisional ionizational equilibrium. Early on, the ionization states are much lower than expected for such hot gas. Later on, the ionization states are higher. This paper also applies the standard observational analyses for determining the color temperature, electron density, and thermal pressure to ROSAT "" observations ÏÏ of one of the simulated remnants, thus providing a map between observational results and physical conditions. The paper reports the O`5, N`4, and C`3 column densities for the simulated remnants. The simulations may be of interest and are applied to studies of the Galactic halo and Local Bubble. They may also be of interest to studies of external galaxies and interarm regions of the Milky Way.