The transmission (T) and phase shift (theta) of 0.2-1.5 THz radiation have been measured simultaneously on unpatterned, high-quality YBa2Cu3O7 films (T-c 90 K) in the normal and superconducting states using a coherent, pulsed, time-domain technique. The complex surface impedance has been extracted without contacting or patterning the superconducting films using T and theta. Above T-c, both the real (R(s)) and imaginary (X(s)) parts show a metallic root omega T dependence with almost equal magnitude as predicted by the normal skin effect. Below T-c, R(s) scales with omega(2), but only for omega/2 pi less than or equal to 400 GHz; it increases more slowly with frequency above 400 GHz. The reactance X(s) is linear in omega for T << T-c, but follows a weaker power dependence with frequency at higher temperatures, indicating that the penetration depth is also frequency dependent. We attribute these features to a rapid decrease of the quasiparticle relaxation rate, 1/tau, in the super-conducting state (where 1/tau is comparable to the photon energy of the THz beam), and a significant influence of the remaining normal carriers in the THz regime. Differences between the microwave and submillimeter-wave responses will be discussed.