Crosslinked thermoset polymers are used heavily in industrial and consumer products, as well as in infrastructure. When used as a protective coating, a thermoset's net-like structure can act as a barrier to protect an underlying substrate from permeation of moisture, salt, or other chemicals that otherwise weaken the coating or lead to substrate corrosion. Understanding how such coatings degrade, both at microscopic and macroscopic scales, is essential for the development and testing of materials for optimal service life. Several numerical and computational techniques are used to analyze the behavior of model crosslinked polymer networks under changing conditions at a succession of scales. Molecular dynamics is used to show the effects of cooling and constraints on cavitation behavior in coarse-grained bulk thermosets, as well as to investigate dynamical behavior under varying degradation conditions. Finite-element analysis is applied to examine strain distributions and loci of failure in several macroscopic coated test panel designs, discussing the effects of flexure and coating stack moduli. Finally, the transport of moisture through model coatings under cycled conditions is examined by lattice Boltzmann numerical techniques, considering several common concentration-dependent diffusivity models used in the literature and suggesting an optimal behavior regime for non-constant diffusivity.