We calculated the Förster resonance energy-transfer (FRET) efficiency of a theoretical host–guest composite formed by all-trans β-cryptoxanthin (BCRY), all-trans zeaxanthin (ZEA), and a zeolite-LTL (Linde Type L) nanochannel with the help of computational chemistry tools. Climate change demands urgently the development of novel renewable energies, and in such a context, artificial photosynthesis arises as a promising technology capable of contributing to satisfying humankind’s energy needs. All artificial photosynthetic devices need antennas to harvest and transfer energy to a reaction center efficiently. Antenna materials integrated by highly fluorescent synthetic pigments embedded onto the nanochannels of a zeolite-LTL have already been shown experimentally to be very efficient supramolecular assemblies. However, research work computing the efficiency of an antenna made of nonfluorescent natural pigments and a zeolite-LTL nanochannel has not been undertaken yet, at least to our knowledge. Fortunately, natural dyes possess outstanding features to study them dynamically; they are environmentally friendly, inexpensive, ubiquitous, and abundant. Density functional theory (DFT) methods were chiefly employed along with the CAM-B3LYP functional and the 3-21G*/6-311+G(d,p) basis sets. The ONIOM method enabled geometry and energy calculations of dyes inside the zeolite-LTL (ZL) nanochannel. The Förster resonance energy-transfer (FRET) efficiency and the Förster radius of the composite were 40.9% and 24.9 Å, respectively. Theoretical findings suggested that this composite might contribute to diminishing costs and improving the environmental friendliness of an antenna system.