Benign termination scenarios—where the runaway (RE) beam is dissipated over a large area of the plasma-facing components—offer a promising pathway for controlled RE mitigation. The success of this technique relies heavily on the properties of the cold, partially ionised plasma coexisting with the RE beam, referred to as the companion plasma. This work presents detailed modelling of companion plasma particle, momentum and energy balance during benign runaway termination experiments conducted on TCV and ASDEX Upgrade (AUG), using the SOLPS-ITER code. SOLPS-ITER is a well-established edge plasma simulation tool, traditionally employed to study power exhaust and divertor physics in tokamaks, which here is used for the first time in runaway-related scenarios. The results demonstrate the capability of SOLPS-ITER to simulate the interaction between the companion plasma, sustained by energy transferred from the RE beam, and the surrounding neutral atoms and molecules following massive material injection (MMI). The modelling successfully reproduces key experimental trends observed in TCV, most notably the reduction in plasma density and temperature with increasing neutral pressure, which are characteristic signatures of effective companion plasma recombination. This approach shows strong potential for enhancing our predictive capabilities regarding RE mitigation strategies in ITER and future reactors. In particular, validating the method across a multi-machine database of low-Z benign termination experiments and subsequently extrapolating to ITER-relevant conditions and geometry could provide a physics-based estimate of the required neutral pressure range for achieving benign terminations in ITER.