Recent advances in nanofabrication technology have facilitated the development of single-walled carbon nanotube (SWCNT) arrays with long-range order across macroscopic dimensions. However, an accurate generalized method of modeling these systems has yet to be realized. A multiscale computational approach combining first principles methods based on density functional theory (DFT) and extensions thereof to account for excited electron states, and classical electrodynamics simulations is described and applied to calculations of the optical properties of macroscopic SWCNT arrays. The first-principles approach includes the use of the GW and Bethe-Saltpeter methods, and the accuracy of these approximations is assessed through evaluation of the absorption spectra of individual SWCNTs. The fundamental mechanisms for the unique characteristics of extremely low reflectivity and high absorptance in the near IR are delineated. Furthermore, opportunities to tune the optical properties of the macroscopic array are explored.