We report quantitative electrical admittance measurements of diffusive superconductor--normal-metal--superconductor (SNS) junctions at gigahertz frequencies and millikelvin temperatures. The gold-palladium-based SNS junctions are arranged into a chain of superconducting quantum interference devices. The chain is coupled strongly to a multimode microwave resonator with a mode spacing of approximately 0.6 GHz. By measuring the resonance frequencies and quality factors of the resonator modes, we extract the dissipative and reactive parts of the admittance of the chain. We compare the phase and temperature dependence of the admittance near 1 GHz to theory based on the time-dependent Usadel equations. This comparison allows us to identify important discrepancies between theory and experiment that are not resolved by including inelastic scattering or elastic spin-flip scattering in the theory.