Infrared-luminous galaxies are important sites of stellar and black hole mass assembly at most redshifts. Their luminosities are often estimated by fitting spectral energy distribution (SED) models to near- to far-infrared data, but the dependence of these estimates on the data used is not well understood. Here, using observations simulated from a well-studied local sample, we compare the effects of wavelength coverage, signal-to-noise ratio, flux calibration, angular resolution, and redshift on the recovery of starburst, active galactic nucleus (AGN), and host luminosities. We show that the most important factors are wavelength coverage that spans the peak in a SED, and dense wavelength sampling. Such observations recover starburst and AGN infrared luminosities with systematic bias below 20%. Starburst luminosities are best recovered with far-infrared observations, while AGN luminosities are best recovered with near- and mid-infrared observations, though the recovery of both are enhanced with near/mid-infrared and far-infrared observations, respectively. Host luminosities are best recovered with near/far-infrared observations, but are usually biased low, by ≳20%. The recovery of starburst and AGN luminosity is enhanced by observing at high angular resolution. Starburst-dominated systems show more biased recovery of luminosities than do AGN-dominated systems. As redshift increases, far-infrared observations become more capable and mid-infrared observations less capable at recovering luminosities. Our results highlight the transformative power of a far-infrared instrument with dense wavelength coverage, from tens to hundreds of microns, for studying infrared-luminous galaxies. We tabulate estimates of systematic bias and random error for use with JWST and other observatories.