This paper introduces a new design approach to mitigate the effect of parasitic capacitances and achieve high performance in large air-gap capacitive wireless power transfer (WPT) systems for electric vehicle (EV) charging. In a capacitive WPT system for EVs, the vehicle chassis and roadway introduce multiple parasitic capacitances that can overwhelm the coupling capacitance and severely degrade power transfer and efficiency. The proposed approach addresses this challenge by employing split-inductor matching networks, which allow the complex network of parasitic capacitances to be simplified into an equivalent four-capacitance model. The shunt capacitances of this model are directly utilized as the matching network capacitors, hence, absorbing the parasitic capacitances and eliminating the need for discrete high-voltage capacitors. A systematic procedure is developed to accurately measure the equivalent capacitances of the model, enabling the system's performance to be reliably predicted. The proposed approach is used to design two 6.78-MHz 12-cm air-gap prototype capacitive WPT systems with capacitor-free matching networks. The first system transfers up to 590 W using 150-cm <
sup>
2<
/sup>
square coupling plates and achieves an efficiency of 88.4%. The second prototype system transfers up to 1217 W using 118-cm <
sup>
2<
/sup>
circular coupling plates, achieving a power transfer density of 51.6 kW/m <
sup>
2<
/sup>
. The measured output power profiles of the two systems match well with their predicted counterparts, validating the proposed design approach.