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We present experimental measurements of SQUID-induced damping effects on strongly coupled, lumped-element resonators in the 500kHz-1 MHz frequency range. While dc SQUIDs are commonly used for sensitive readout of electromagnetic signals such as in lumped-element axion dark matter searches, coupling a dc SQUID to a resonant circuit modifies the circuit's resonance frequency, quality factor, noise, and impedance. These parameters have a direct impact on the science reach of axion dark matter detectors, making it important to understand SQUID damping contributions. We describe a helium dip probe and two-stage SQUID readout scheme used to probe SQUID damping effects. Measurements from this setup inform the design and operation of both future test platforms as well as next-generation dark-matter experiments.