Measurements and analysis of a radio-frequency planar antenna are presented for applications in inductively-coupled plasma processing. The network of inductive and capacitive elements exhibits high currents under resonance which are efficient for plasma generation. Mode frequencies and impedances are accurately calculated by accounting for the mutual partial inductances using the impedance matrix. The effect of plasma inductive coupling on mode frequency shift and mode impedance is estimated using the complex image method, giving good agreement with experiment. It is proposed that the complex image method combined with the partial inductance concept (see the accompanying paper, Part I (Howling et al 2015 Plasma Sources Sci. Technol. 24 065014)) offers a general way to calculate the impedance characteristics of inductively-coupled plasma sources in planar geometry.