We model SNRs at a variety heights above the disk with a detailed numerical simulation that includes non-equilibrium ionization and recombination and follows the remnants' evolution until their hot bubbles have cooled. We analytically calculate the bubbles' buoyant acceleration and frictional drag. From the simulation results, combined with the rates for isolated supernova explosions above a height of 130 pc, we estimate the time and space average O+5, N+4, and C+3 column densities and emission intensities, 1/4 keV soft X-ray surface brightness, area coverage, and volume occupation due to the population of isolated SNRs above the Galaxy's H (I) layer. Irrespective of assumed supernova explosion energy, ambient nonthermal pressure, or frictional drag coefficient used in the calculations, the predicted O+5 column density as a function of height matches the observed distribution between 130 and 2000 pc. The O VI resonance line emission (lambda lambda 1032, 1038) contributes significantly to the average observed intensity. Assuming our modest supernova explosion rate, the population of isolated extraplanar SNRs can explain 80% of the observed 1/4 keV surface brightness attributed to the extraplanar gas beyond the H (I) layer in the southern hemisphere. Within the range of uncertainty in the SN rate, such SNRs can explain all of this observed emission (400 x 10(-6) counts s(-1) arcmin(-2)). Thus, extraplanar SNRs could be the most important sources of hot gas between the Local Bubble and z similar to 2000 pc in the relatively quiescent southern hemisphere. These results stand whether the remnants are assumed to be buoyant or not. The population of old extraplanar SNRs should cover most, but not all of the high-latitude sky, thus explaining the mottled appearance of the soft X-ray maps ( outside of superbubbles). Bright young extraplanar SNRs should cover less than 1% of the high-latitude sky. Perhaps the l = 247 degrees, b = -64 degrees crescent in the 1/4 keV X-ray maps could be such a remnant.
