The quantum circuit rule (QCR) allows estimation of the conductance of molecular junctions, electrode|X-bridge-Y|electrode, by considering the molecule as a series of independent scattering regions associated with the anchor groups (X, Y) and bridge, provided the numerical parameters that characterise the anchor groups (a _X, a _Y) and molecular backbones (b _B) are known. Single-molecule conductance measurements made with a series of α,ω-substituted oligoynes (X-{(C ≡ C) _N}-X, N = 1, 2, 3, 4), functionalised by terminal groups, X (4-thioanisole (C ₆H ₄SMe), 5-(3,3-dimethyl-2,3-dihydrobenzo[b]thiophene) (DMBT), 4-aniline (C ₆H ₄NH ₂), 4-pyridine (Py), capable of serving as ‘anchor groups’ to contact the oligoyne fragment within a molecular junction, have shown the expected exponential dependence of molecular conductance, G, with the number of alkyne repeating units. In turn, this allows estimation of the anchor (a _i) and backbone (b _i) parameters. Using these values, together with previously determined parameters for other molecular fragments, the QCR is found to accurately estimate the junction conductance of more complex molecular circuits formed from smaller components assembled in series.