The optical properties of chromophores embedded in a water-solvated dimer of octa-acid that forms a molecular-shaped capsule are investigated. In particular, we address the anisotropic dielectric environment that appears to blue-shift excitation energies compared to the free aqueous chromophores. Recently we reported that using an effective scalar dielectric constant epsilon approximate to 3 appears to reproduce the measured spectra of the embedded coumarins, suggesting that the capsule provides a significant, albeit not perfect, screening of the aqueous dielectric environment. Here, we report absorption energies using a theoretical treatment that includes continuum solvation affected by an anisotropic dielectric function reflecting the high-dielectric environment outside of the capsule and the low-dielectric region within. We report time-dependent density functional theory calculations using a range-separated functional with the Poisson boundary conditions that model the anisotropic dielectric environment. Our calculations find that the anisotropic environment due to the water-solvated hydrophobic capsule is equivalent to a homogeneous effective dielectric constant of approximate to 3. The calculated values also appear to reproduce measured absorption of the embedded coumarin, where we study the effect of the hydrophobic capsule on the excited state.