Is there a correlation between the (hetero)aromaticity of the core of a molecule and its conductance in a single molecular junction? To address this question, which is of fundamental interest in molecular electronics, oligo(arylene-ethynylene) (OAE) molecular wires have been synthesized with core units comprising dibenzothiophene, carbazole, dibenzofuran and fluorene. The biphenyl core has been studied for comparison. Two isomeric series have been obtained with 4-ethynylpyridine units linked to the core either at para-para positions (para series 1-5) or meta-meta positions (meta series 6-10). A combined experimental and computational study, using mechanically controlled break junction measurements and density functional theory calculations, demonstrates consistently higher conductance in the para series compared to the meta series: this is in agreement with increased conjugation of the π-system in the para series. Within the para series conductance increases in the order of decreasing heteroaromaticity (dibenzothiophene < carbazole < dibenzofuran). However, the sequence is very different in the meta series, where dibenzothiophene ≈ dibenzofuran < carbazole. Excellent agreement between theoretical and experimental conductance values is obtained. Our study establishes that both quantum interference and heteroaromaticity in the molecular core units play important and inter-related roles in determining the conductance of single molecular junctions.