Abstract: Spectral observations of highly ionized elements in the solar corona indicate temperatures of order 106 K, nearly three orders of magnitude larger than photospheric temperatures. Numerous competing theories have proposed plausible mechanisms for sustaining these temperatures, but no consensus has yet been reached. I use satellite observations from the Yohkoh Soft X-ray Telescope (SXT) to provide observational constraints on possible heating mechanisms. I take a forward-modeling approach, using a parameterized approximation for existing coronal heating theories to predict soft X-ray emissions from individual observed solar active regions. Theories that predict observed emissions well are favored over theories that make poor predictions. The forward model begins with a photospheric vector magnetic field measurement of an active region. To solve for the coronal magnetic field, I use a non-constant-alpha force-free field model. I choose several thousand magnetic fieldlines to represent the loop-like structures along which plasma is observed in the solar corona. Along each loop, I solve steady-state equations of mass, momentum, and energy conservation to determine thermodynamic quantities such as temperature and density. Taking into account satellite location and instrument response, I use these results to predict the expected coronal emissions from the active region in question, as observed by SXT. I evaluate 10 case study active regions using 4 heating parameterizations. I find that the predictions of a volumetric heating rate that scales proportionally with average loop field strength and inversely with loop length come closest to matching observed emissions. This parameterization is most similar to the steady-state scaling of two proposed heating mechanisms: van Ballegooijen's 'current layers' theory, taken in the AC limit where loop footpoint motions are rapid compared to Alfvén travel times, and Parker's 'critical angle' mechanism, taken in the case where the angle of misalignment is a twist angle. Although this parameterization best matches the observations, it does not match well enough to make a definitive statement on the nature of coronal heating. Nevertheless, I conclude that my method is a promising approach for studying heating in the absence of direct observational signatures, and I outline the improvements needed to make further progress.