Covalent functionalization of single-walled carbon nanotubes (SWCNTs) introduces red-shifted emission features in the near-infrared spectral range due to exciton localization around the defect site. Such chemical modifications increase their potential use as near-infrared emitters and single-photon sources in telecommunications applications. Density functional theory (DFT) studies using finite-length tube models have been used to calculate their optical transition energies. Predicted energies are typically blue-shifted compared to experiment due to methodology errors including imprecise self-interaction corrections in the density functional and finite-size basis sets. Furthermore, artificial quantum confinement in finite models cannot be corrected by a constant-energy shift since they depend on the degree of exciton localization. Herein, we present a method that corrects the emission energies predicted by time-dependent DFT. Confinement and methodology errors are separately estimated using experimental data for unmodified tubes. Corrected emission energies are in remarkable agreement with experiment, suggesting the value of this straightforward method toward predicting and interpreting the optical features of functionalized SWCNTs.