The optical, electronic, and (photo) catalytic properties of covalent organic frameworks (COFs) are largely determined by their electronic structure and, specifically, by their Frontier conduction and valence bands (VBs). In this work, we establish a transparent relationship between the periodic electronic structure of the COFs and the orbital characteristics of their individual molecular building units, a relationship that is challenging to unravel through conventional solid-state calculations. As a demonstration, we applied our method to five COFs with distinct framework topologies. Our approach successfully predicts their first-principles conduction and VBs by expressing them as a linear combination of the Frontier molecular orbitals localized on the COF fragments. We demonstrate that our method allows for the rapid exploration of the impact of chemical modifications on the band structures of COFs, making it highly suitable for further application in the quest to discover new functional materials.