Magnetic susceptibility and nuclear magnetic shielding at the nuclei of bis-heteropentalenes formed by two furan units ([2,3-b], [3,2-b], [3,4-b], and [3,4-c] isomers) have been computed by several approximated techniques and a large Gaussian basis set to achieve near Hartree-Fock estimates. Ab initio models of the ring currents induced by a magnetic field normal to the molecular plane were obtained for the three isomeric systems of higher symmetry, showing that the pi electrons give rise to intense diamagnetic circulation. The pi currents are responsible for enhanced magnetic anisotropy and strong out-of-plane proton deshielding. The theoretical findings are used to build up a "diatropicity matrix" for two fused five-membered heterocyclic systems.