Terahertz spectroscopy, a noninvasive and non-destructive analytical technique used in art conservation and restoration, can provide compelling data concerning the composition and condition of culturally valuable and historical objects. Terahertz spectral databases of modern and ancient artists' pigments exist but lack explanations for the origins of the unique spectral features. Solid-state density functional theory simulations can provide insight into the molecular and intermolecular forces that dominate the observed absorption features as well as reveal deviations from simple harmonic vibrational behavior that can complicate these spectra. The characteristic terahertz spectra of solid azurite, malachite, and verdigris are presented here, along with simulations of their crystalline structures and sub-3.0 THz lattice vibrations. The powerful combination of theory and experiment enables unambiguous spectral assignment of these complex materials and highlights the challenges that anharmonic peak broadening in organic-containing materials may present in the construction of reference pigment databases.