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Resonance characteristics of fiber-optic ring resonators, e,g., the finesse, are mainly determined by the loss and the coupling coefficient of the fused tapered coupler within the resonator. From measuring the resonance characteristics these parameters can be evaluated nondestructively. This is demonstrated by investigating spliceless nonpolarization maintaining ring resonators using an automated measurement system with an enhanced accuracy by numerical approximation of the resonance dip. Standard deviations of the finesse below 1%, of the coupling factor below 0.1% and of the loss coefficient below 0.01% have been achieved.