Gravitational waves (GW) emitted by binary systems allow us to perform precision tests of general relativity in the strong field regime. Ringdown signals allow for probing black hole mass and spin with high precision in GW astronomy. With improvements in current and next-generation GW detectors, developing likelihood-free parameter inference methods is crucial. This is especially important when facing challenges such as non-standard noise, partial data, or incomplete signal models that prevent the use of analytical likelihood functions. In this work, we propose an amortized simulation-based inference strategy to estimate ringdown parameters directly. Specifically, our method is based on amortized neural posterior estimation, which trains a neural density estimator of the posterior for all data segments within the prior range. The results show that our trained amortized network achieves statistically consistent parameter estimates with valid confidence coverage compared to established Markov-chain methods, while offering inference speeds that are orders of magnitude faster. Furthermore, we evaluate the robustness of the method against transient noise contamination. Our results indicate that the timing of glitch injection significantly affects estimation bias, in particular when the glitch contaminates the early, high-amplitude portion of the signal. Glitch strength is positively correlated with estimation error, but has limited effect at low signal-to-noise ratios. Mass and spin parameters are most sensitive to noise. This study not only provides an efficient and accurate inference framework for ringdown analysis but also lays a foundation for developing robust data-processing pipelines for future GW astronomy in realistic noise environments.