This paper is the first in a series in which the behaviour of the electrical impedance of metals at low temperatures and very high frequencies will be considered from experimental and theoretical standpoints. The technique of resonator measurements at 1200 Mcyc./sec. is described in detail, and experimental curves are given showing the variation with temperature of the r.f. resistivities of superconducting tin and mercury. In contrast to the behaviour of superconductors in static fields, a finite resistance is present at all temperatures, tending as the absolute zero is approached to a very low value, which is probably zero for mercury but not for tin. The experimental results are in good agreement with London's measurements on tin by a different method. The latter's observation, that the r.f. resistance of normal tin above the transition point is much greater than that predicted from the classical skin-effect theory, is confirmed, and a similar, though less marked, effect is found also for mercury.