In this paper, a frequency-domain characterisation of the period-doubling bifurcation is proposed. This allows an efficient detection and localisation of such points along frequency-response curves computed through continuation and the harmonic balance method. A simple strategy for branch switching to sub-harmonic regimes is presented as well. Furthermore, these bifurcations are tracked in a two-dimensional parameter space, and extremum points with respect to the tracking parameter are characterized and linked to sub-harmonic isola formation. As a test case for these methods, a forced Duffing oscillator with asymmetric clearances is studied numerically. The results, which include the prediction of period-doubling cascades and sub-harmonic isolas, are then compared to experimental results, yielding an excellent agreement.