The excitation of non-TEM modes around the ITER ICRF (ion cyclotron range of frequency) antenna plug can considerably increase the level of RF currents and voltages on the ITER plug. We report on a study of these modes and a solution to avoid them in the ITER ion cyclotron range of frequencies. From a transmission line approach we show that resonances can be avoided if the distance between the mouth of the line and an added short-circuit is sufficiently small. We therefore propose to position short-circuits at about 1 m from the antenna mouth, constituted by rows of closely spaced non-capacitive contacts all around the plug. These conclusions are further validated with Microwave Studio® simulations. A simplified model of the ITER ICRF array is used for comparing various grounding solutions and it is proved that the solution already inferred from transmission line approximation suppresses the resonances from the frequency domain relevant for ICRH in ITER. The MWS calculations predict that the proposed solution also avoids large RF currents in the blanket modules and in their connectors. Their amplitude barely exceeds 5% of the strap RF currents. This solution avoids perturbation of the antenna array impedance matrix by the coaxial gap. We also discuss resonances appearing at harmonic frequencies which could be excited by various non-linear effects due to the plasma or the generator. This kind of excitation should not lead to large voltage build-up.