We propose cyclic 5- and 7-ring structures with alternating single and double bonds and adjacent imino and amino groups as candidates for switches in molecular electronics, with amino-imino tautomerisation as the switching mechanism. Due to the C2V-symmetric transition state, the molecules exhibit a symmetric double-well potential with identical energies for the two states, which is a desirable property for a functioning molecular switch. Calculations at the double hybrid mPW2PLYP-D2/def2-TZVP level show barriers of 1.07 and 0.52 eV for the 5-ring and 7-ring, respectively (zero-point corrected: 0.97 and 0.41 eV, respectively). The corresponding 9-ring structure is not suitable as a molecular switch, due to ring puckering and the existence of multiple minima. Attachment of ethyne groups to the nitrogens and the opposite carbon, as models for molecular wires, only slightly changes the barrier heights. The 5- and 7-ring structures are promising switch candidates for further investigation.