The impedance and emission properties of capacitively coupled Hg‐Ar discharges have been studied in order to determine the limitations of efficiency and radiance of the Hg UV radiation. The background is an application in electrodeless discharge lamps. The Ar pressure was varied between 40 and 1330 Pa, the frequency range was 10–400 MHz. The radiation efficiency generally increases with frequency, in particular at low Ar pressure and high rf power. It is correlated with the variation of the resistive impedance component with rf current and frequency. The results are discussed in terms of a discharge structure consisting of a positive column‐like bulk plasma and two rf sheaths. The frequency dependence is mainly caused by the power dissipation in the non‐luminous sheaths. The power share between bulk plasma and sheaths is determined by a suitable impedance analysis. At high power densities, the efficiency is additionally limited by saturation phenomena. Efficiencies comparable to those known from conventional, electroded discharges can be obtained by a proper choice of parameters such as discharge current and operating frequency. The measurements of the Hg UV radiation are supplemented by a spatially resolved spectroscopy of the Ar excitation. The extension of the dark spaces corresponds to the sheath thicknessdsas derived from the impedance data.dsvaries with Ar pressurepArand frequency  fapproximately as (pAr)−1/3f−1/2. A recently described model for the power dissipation in the sheath of capacitively coupled rf discharges in Ar is also in good agreement with the impedance data of Hg‐Ar discharges. The complex sheath impedance is represented by a semi‐empirical, analytical expression over a wide range of Ar pressures and frequencies.