In previous work, a magnetically modulated microwave absorption (MMMA) technique to measure the Ginzburg-Landau parameter kappa = (lambda/zeta) in high-T(c) superconductors (bulk samples of YBCO) was described. In this work, how this technique can be applied to the measurement of the London penetration depth lambda is described. Data are reported for the temperature variation of lambda in a well-characterized c-axis-oriented polycrystalline thin film of YBa2Cu3O7-x, prepared by a pulsed laser deposition technique. For low temperatures, lambda(O) congruent-to 3640 angstrom with the microwave electric field oriented parallel to the c axis. The temperature dependence of lambda(O)/lambda(T) can be well described by the two-fluid model. The data are also reasonably fit by a BCS model, however the MMMA technique (in the work here reported) does not have the resolution at low temperatures to obtain strong quantitative evidence for an energy gap DELTA (even if it exists).