Conjugated-circuit (CC) models are simple and efficient approaches for approximating the aromaticity of a system, as described via application of the magnetic criterion by the presence of ring currents. Unfortunately, this class of current model is often inferior to the well-established H¨uckel-London model, failing to account for non-Kekul´ean, bond-fixed or charged systems. The Aihara variant of the H¨uckel-London model is employed as a tool to examine cycle contributions and provides a useful understanding of observed ring current effects based on orbital occupancy. Detailed analysis of the Aihara formalism allowed examination of heterocyclic monocycles, indicating that current is robust against changes in electronegativity. Variation in current maps for perylene and related structures, in ipsocentric, pseudo-p, H¨uckel-London and conjugated-circuit models was also rationalised. The major inconsistency in conjugated circuit current maps is identified as the result of inherent exclusion of important non-conjugated contributions. To address various shortcomings, two extended 'conjugated-circuit' models are proposed to reproduce H¨uckel-London accurate maps. The first involves a parameterised contribution from circuits in Dewar structures, representing the contribution from first-excited structures to a given cycle. The second (the Myrvold-Fowler models) involves ratios of coefficients from the characteristic polynomials of the graph and cycle-removed graph, inspired from the Aihara model. Both models offer a way to include, for the first time, non-Kekul´ean systems in CC models, resulting in more accurate current maps. The Adjusted Myrvold-Fowler model is found to 'best' approximate H¨uckel-London current magnitudes for a variety of benzenoid systems.