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The single–molecule conductance of a series of BN-acene-like derivatives has been measured by using scanning tunneling break-junction techniques. A strategic design of the target molecules has allowed us to include azaborine units in positions that unambiguously ensure electron transport through both heteroatoms, which is relevant for the development of customized BN-doped nanographenes. We show that the conductance of the anthracene azaborine derivative is comparable to that of the pristine all-carbon anthracene compound. Notably, this heteroatom substitution has also allowed us to perform similar measurements on the corresponding pentacene-like compound, which is found to have a similar conductance, thus evidencing that B–N doping could also be used to stabilize and characterize larger acenes for molecular electronics applications. Our conclusions are supported by state-of-the-art transport calculations., This work has been supported by the MICINN projects PID2019-105458RB-I00, PID2019-106732GB-I00, PGC2018-101873-A-I00, CTQ2017-85454-C2-1-P, FIS2016-77889-R and MAT2017-88693-R, the European Research Council (ERC) (677023), the FEDER/Junta de Andalucía project A-FQM-221-UGR18 and the Comunidad de Madrid project NanoMagCOST (CM S2018/NMT-4321). We also thank Severo Ochoa Programme for Center of Excellence in R&D (SEV-2016-0686) and María de Maeztu Programme for Units of Excellence in R&D (CEX2018-000805-M). We acknowledge the allocation of computer time by the Red Española de Supercomputación and the Centro de Computación Científica at the Universidad Autónoma de Madrid (CCC-UAM). J.G.F. thanks the PFI program of the MICINN co-financed by the European Social Fund. I.R.M. thanks MICINN for a Personal Técnico de Apoyo contract (PTA2017-13681-I). E.L. thanks the Comunidad de Madrid grant Atracción de Talento 2019-T1/IND-16384.