We investigate quantum interference in the transport properties of porphyrin-based molecular devices, and are able to develop a minimal but qualitatively accurate model of conductance based on the maximally localized Wannier functions of just the isolated molecule. We find that transmission at or near the Fermi level can be engineered to vary by orders of magnitude in response to hydrogen tautomerization in the inner ring, a recently developed experimental capability. This allows us to suggest that tape porphyrins can act as molecular-size memory units, displaying many-valued logic.