Perovskite/silicon tandem solar cells have a tremendous potential to boost renewable electricity production thanks to their very high performance combined with promising cost structure. However, for actual field deployment, any solar cell technology needs to be assembled into modules, where the associated processes involve several challenges that may affect both the performance and stability of the devices. For instance, due to its hygroscopic nature, ethylene vinyl acetate (EVA) is incompatible with perovskite-based photovoltaics. To circumvent this issue, we investigate here two alternative encapsulant polymers for the packaging of perovskite/silicon tandems into minimodules: a thermoplastic polyurethane (TPU) and a thermoplastic polyolefin (TPO) elastomer. To gauge their impact on tandem-module performance and stability, we performed two internationally established accelerated module stability tests (IEC 61215): damp heat exposure and thermal cycling. Finally, to better understand the thermomechanical properties of the two encapsulants and gain insight into their relation to the thermal cycling of encapsulated tandems, we performed a dynamic mechanical thermal analysis. Our understanding of the packaging process of the tandem module provides useful insights for the development of commercially viable perovskite photovoltaics.