Current-voltage, or i–V, curves are used in combustion to characterise the ionic structure of flames. The objective of this paper is to develop a detailed modelling framework for the quantitative prediction of the i–V curves in methane/air flames. Ion and electron transport coefficients were described using methods appropriate for charged species interactions. An ionic reaction mechanism involving cations, anions and free electrons was used, together with up-to-date rate coefficients and thermodynamic data. Because of the important role of neutral species in the ion production process, its prediction by the detailed AramcoMech 1.4 mechanism was optimised by using available experimental measurements. Model predictions were evaluated by comparing to i–V curves measured in atmospheric-pressure, premixed, burner-stabilised flames. A detailed evaluation of the reliability of ion kinetic and transport parameters adopted was performed. The model provides good quantitative agreement with experimental data for various conditions.