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Purpose – The purpose of this paper is to discuss a numerically efficient simulation method for the study of the high-frequency behaviour of air-cored coils. The self-resonance phenomenon of coils can be studied which is important, e.g., in wireless power transfer (WPT). Design/methodology/approach – A full-wave and a quasi-stationary integral formulation is introduced. The integral equation is solved by using the Method of Moments. The complex impedance of the coil is calculated and studied in a wide frequency band. Findings – The integral equation method is numerically efficient compared to finite element schemes, making possible its use in design optimisation problems. Research limitations/implications – The present model can treat homogeneous media only. Future research will focus on the extension of the approach to heterogeneous media. Practical implications – The method can be used in the design optimisation of WPT systems that apply magnetically coupled resonant coils. Originality/value – The presented computation scheme is original. Integral equation schemes have not been used for coil modelling before, to the best of the author’s knowledge. [ABSTRACT FROM AUTHOR]