W sputtering during ICRF on ASDEX Upgrade (AUG) and temperature rise on JET A2 antenna septa are considered in connection with plasma conditions at the antenna plasma facing components and E|| near-fields. Large antenna-plasma clearance, high gas puff and low light impurity content are favorable to reduce W sputtering in AUG. The spatial distribution of spectroscopically measured effective W sputtering yields clearly points to the existence of strong E|| fields at the antenna box ("feeder fields") which dominate over the fields in front of the antenna straps. The picture of E|| fields, obtained by HFSS code, corroborates the dominant role of E|| at the antenna box on the formation of sheath-driving RF voltages for AUG. Large antenna-plasma clearance and low gas puff are favourable to reduce septum temperature of JET A2 antennas. Assuming a linear relation between the septum temperature and the sheath driving RF voltage calculated by HFSS, the changes of the temperature with dipole phasing (00pp, 0pp0 or 0p0p) are well described by the related changes of the RF voltages. Similarly to the AUG antenna, the strongest E|| are found at the limiters of the JET A2 antenna for all used dipole phasings and at the septum for the phasings different from 0p0p. A simple general rule can be used to minimize E|| at the antenna: image currents can be allowed only at the surfaces which do not intersect magnetic field lines at large angles of incident. Possible antenna modifications generally rely either on a reduction of the image currents, on their short-circuiting by introducing additional conducting surfaces or on imposing the E|| = 0 boundary condition. On the example of AUG antenna, possible options to minimize the sheath driving voltages are presented.