The pulp and paper (P&P) industry holds significant global importance. However, the industry’s processes substantially demand water and energy resources. Consequently, there is a pressing need for the industry to adopt more sustainable production practices, aiming to trim environmental impact and strengthen resilience against climate change. Recent research has highlighted the potential for substantial increases in Swedish biogas production using anaerobic wastewater (WW) treatment methods within P&P mills. The P&P sector traditionally relies on aerobic biological WW treatment, overlooking the valuable opportunity for WW resource recovery. This study aims to evaluate anaerobic moving bed biofilm reactors (AnMBBR) to enhance energy recovery while enabling treatment capacity for the P&P industry’s anaerobic WW treatment. The results of this study showed the resilience of the AnMBBR system. It proved capable of recovering from overload conditions and operating even during prolonged periods at low pH levels. However, the system removes mainly soluble COD, suggesting higher capabilities on P&P WW with a high fraction of soluble COD. Its ability to produce methane-rich biogas demonstrates efficient gas production while maintaining simple operational procedures.