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The temperature dependence of the magnetic penetration depth of Bi2Sr2CaCu20g single crystals and YBa2Cii307-s thin films has been measured with a parallel plate resonator technique at microwave frequencies. Both materials show a T 2 temperature dependence between 10 and 25 K, and systematic deviations towards a flatter temperature dependence below 10 K. We have also calculated the real part of the complex conductivity of YBa2Cu307-$ thin films from our penetration depth and surface resistance data and compare them with those of YBa2Cu3C>7-a single crystals.