Model order reduction (MOR) can play a pivotal role in reducing the cost of repeated computations of large thermo-acoustic models required for comprehensive stability analysis and optimization. In this proof-of-concept study, acoustic wave propagation is modeled with a one-dimensional (1D) network approach, while acoustic–flame interactions are modeled by a flame transfer function (FTF). Three reduction techniques are applied to the acoustic subsystem: firstly modal truncation (MT) based on preserving the acoustic eigenmodes, and then two approaches that strive to preserve the input–output transfer behavior of the acoustic subsystem, i.e., truncated balanced realization (TBR) and iterative rational Krylov algorithm (IRKA). After reduction, the reduced-order models (ROMs) are coupled with the FTF. Results show that the coupled reduced system from MT accurately captures thermo-acoustic cavity modes with weak influence of the flame, but fails for cavity modes strongly influenced by the flame as well as for intrinsic thermo-acoustic (ITA) modes. On the contrary, the coupled ROMs generated with the other two methods accurately predict all types of modes. It is concluded that reduction techniques based on preserving transfer behavior are more suitable for thermo-acoustic stability analysis.