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Frequency weighted model reduction framework pretested by Enns yields an unstable reduced order model. Researchers demonstrated several stability preserving techniques to address this main shortcoming, ensuring the stability of one-dimensional and two-dimensional reduced-order systems; nevertheless, these approaches produce significant truncation errors. In this article, Gramians-based frequency weighted model order reduction frameworks have been presented for the discrete-time one-dimensional and two-dimensional systems. Proposed approaches overcome Enns&#x2019; main shortcoming in reduced-order model instability. In comparison to the various stability-preserving approaches, proposed frameworks provide an easily measurable <italic>a priori</italic> error-bound expression. The simulation results show that proposed frameworks perform well in comparison to other existing stability-preserving strategies, demonstrating the efficacy of proposed frameworks.