In this Letter, we present resonance properties in terahertz metamaterials consisting of a split-ring resonator array made from high-temperature superconducting films. By varying the temperature, we observe efficient metamaterial resonance switching and frequency tuning. The results are well reproduced by numerical simulations of metamaterial resonance using the experimentally measured complex conductivity of the superconducting film. We develop a theoretical model that explains the tuning features, which takes into account the resistive resonance damping and additional split-ring inductance contributed from both the real and imaginary parts of the temperature-dependent complex conductivity. The theoretical model further predicts more efficient resonance tuning in metamaterials consisting of a thinner superconducting split-ring resonator array, which are also verified in subsequent experiments.