In this article, a novel Bayesian framework is proposed for real-time system identification with calibratable model classes. This self-calibrating scheme adaptively reconfigures the model classes to achieve reliable real-time estimation for the system state and model parameters. At each time step, the plausibilities of the model classes are computed and they serve as the cue for calibration. Once calibration is triggered, all model classes will be reconfigured. Thereafter, identification will continue to propagate with the calibrated model classes until the next recalibration. Consequently, the model classes will evolve and their deficiencies can be corrected adaptively. This remarkable feature of the proposed framework stimulates the accessibility of reliable real-time system identification. Examples are presented to demonstrate the efficacy of the proposed approach using noisy response measurement of linear and nonlinear time-varying dynamical systems under stationary condition.