This chapter introduces an interval-based reduced-order model (IROM) framework designed to handle high-dimensional linear systems subject to unknown-but-bounded (UBB) parameter uncertainties. In contrast to conventional probabilistic techniques that require extensive sampling of data, the proposed method leverages interval analysis to ensure robustness in data-sparse scenarios. The formulation begins by establishing interval state-space equations, which are then converted to a balanced realization form to preserve system invariants. To accurately quantify the uncertainty propagation, bounds of the observability and controllability Gramians, and the Hankel singular values (HSVs), are derived using interval Lyapunov equations and a customized interval perturbation-based singular value decomposition (SVD) technique. Furthermore, addressing the issue of dense interval distributions of HSV in the system, a novel truncation criterion based on interval possibility theory is developed to objectively determine the optimal reduced order. Numerical validations involving mechanical systems demonstrate that the IROM approach achieves approximation accuracy comparable to Monte Carlo simulations (MCSs) while offering superior computational efficiency.