Abstract Physics-based models of lithium-ion battery dynamics are developed from fundamental electrochemical principles and describe cell internal electrochemical variables in addition to terminal voltage. Real-time estimates of the values taken on by internal cell variables provided by such models might be leveraged by future battery-management systems to control fast-charging and routine use of a battery pack to maximize performance but minimize aging. These models are most naturally described as sets of coupled partial-differential equations (PDEs), and so the greatest obstacle to their adoption stems from the computational complexity involved in finding solutions to the model equations. To make a feasible physics-based model for battery management, we must construct reduced-order approximations to these PDE models. In this paper, we present four methods to find high-fidelity discrete-time state-space reduced-order models (ROMs) that approximate infinite-order transcendental transfer functions that model the PDE relationships of all electrochemical variables of interest. These four methods are compared for a single cell based on speed, memory usage, robustness, and accuracy of the predictions of the resulting reduced-order models with respect to precise numerical simulations of the PDEs. We find that all four methods produce ROMs that match the linearized PDEs closely in the frequency domain and that yield time-domain simulations that match those from the nonlinear PDEs as well, but that each xRA method has distinct features so that different applications might prefer one method versus another.