A penetration depth (λ) measurement technique, which is based upon the λ-dependence of the propagation velocity of electromagnetic waves in superconducting transmission lines, is refined and used to accurately measure λ's in Pb films containing Au, In, or Bi additions. The results are applied to test two distinct predictions for λ's in London (or type II) superconductors. First, the measured dependence of λ upon low temperature electrical resistivity is compared with the theoretical prediction for a type II superconductor containing a dilute homogeneous impurity concentration. We find that the measured λ's follow this simple prediction reasonably well, irrespective of the species of impurity, with two anticipated exceptions. Namely, deviations occur for pure Pb, which is not a type II superconductor, and for the highest impurity concentration, in which case the Fermi surface may be appreciably distorted from that of pure Pb. Second, the London-theory prediction for the dependence of the effective penetration depth (λeff) upon film thickness (d), λeff= λ(T) coth d/λ(T), is tested, in a d/λ range in which coth d/λ, is not closely approximated by 1 or λ/d. Separate experiments in which either film thickness or temperature, T, are varied reveal excellent agreement with the above formula. To our knowledge this is the first detailed confirmation of this explicit hyperbolic cotangent dependency.