Microwave Measurements of Giant Magnetoresistance*

~A measurement of the GMR effect seen in the reflection and transmission coefficients of a film placed in a rectangular microwave waveguide bridge is presented. ~The relative change in transmission coefficient is found to be nearly a factor of 2 larger than the transport GMR effect while the change in reflection coefficient is of opposite sign and an order of magnitude smaller. ~A full treatment of the reflection and transmission coefficients, considering both the interfaces and the decay of the fields within the layers, provides a quantitative relationship to the transport GMR with no free parameters. ~We describe this model and show agreement with experiment.