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I think the ring resonator method is best suited for your problem. I don't have time now to search for the papers, maybe this hint will help.
The essence is to couple input and output striplines to a 1-wavelength ring resonator resonating at 1-2 GHz. It will have sharp resonances repeating at almost equidistant frequencies as well. You can mesure transmission (S21) up to 30-40 GHz depending of your interest. The geometrical length is fixed, so you can determine Er at each resonance from the resonance condition and Tand from the Q factor. Of course, it is the integral Q including dielectric and metal loss.
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