A multi-scale and multi-physics finite element analysis is performed on the electro-chemically coupled ion transport. The goal is to predict the electro-chemical performance of the Structural Battery Electrolyte (SBE), which is a porous polymer skeleton filled with a liquid electrolyte. This is achieved by exploiting computational homogenization and Model Order Reduction (MOR) based on Proper Orthogonal Decomposition (POD). In the FE analysis, a sub-scale Representative Volume Element (RVE) is used in a two-scale modeling approach. The balance equations are Gauss' law and mass balance of the pertinent ions. Linearized constitutive relations with coupling effects are used. Periodic boundary conditions are imposed on the primary fields of the RVE model, i.e., the electrical and the chemical potential fields. By solving the fully coupled electro-chemical RVE problem for various loading cases, we are able to collect snapshots that serve as training data for POD. The goal of the POD-based MOR framework is to train a surrogate model which replaces RVE computations. The benefit of the surrogate model is that it requires less computational effort compared to the full RVE problem. In this contribution, we investigate how the choice of training data and POD modes affect the simulation accuracy. Finally, we also demonstrate the speed-up obtained by exploiting the surrogate model.