We characterize the attachment of excess-electrons to organic nanoporous systems such as molecular nanohoops and models of covalent organic frameworks (COFs) using many-body methods. All the nanopore systems exhibit diffuse electronic states where the excess-electron is bound to the molecular scaffold via long-range polarization forces, and the excess-electron is predominantly localized in the interior of the nanopore or away from the molecular scaffold. Such ``nanopore-bound'' states show an enhanced electron-transfer coupling compared to more strongly-bound skeletal-states (or valence-bound states), where the excess-electron is confined to the molecular skeleton. For 1D assemblies of nanohoops, the bands formed from nanopore-bound states have a consistent nearly-free-electron character, indicating an efficient excited-state pathway for charge-carriers, while the bands from skeletal-states have higher effective mass along certain lattice directions. The nanopore-bound states show distinct size-dependent variations in electron affinities compared to skeletal-states and previously observed molecular quantum corral states. We conclude that nanopore-bound states emerge from polarization-induced quantum confinement, forming a distinct common feature of organic nanoporous matter with potential for efficient electron-transport.