The tunable delay of the silicon nitride micro-ring can be indirectly obtained by measuring the phase characteristics with the high-frequency resolution optical vector-network analysis method. However, the delay-spectrum-measurement stability of the silicon nitride micro-ring is seriously affected by some factors such as phase noise, laser-carrier-frequency fluctuation, and signal-to-noise ratio of the measurement system. This study experimentally analyzes these effects on the delay spectrum measurement of the silicon nitride micro-ring. By optimizing the measurement system and data processing method, a high-resolution measurement is achieved with delay and extinction ratio resolutions of approximately 10 ps and 0.04 dB, respectively. This work provides important reference value for the silicon nitride micro-ring measurement and paves the way for its applications in microwave photonic beamforming systems.