The EU aims to be climate-neutral by 2050, meaning that greenhouse gas emissions are to be net-zero. Sweden has good potential for net-negative emissions using carbon capture technologies in biomass-based district heating production systems. However, capturing CO₂ from flue gases requires heat and electricity, which affects net outputs of heat and electricity from combined heat and power plants. In this study, district heating production in the Swedish city of Gävle is modeled using linear programming. The impact of installing carbon capture technologies on two different production plants is investigated. Changes in fuel use, heat and electricity production and global CO₂ emissions are calculated. The results show that between 151 and 506 ktonnes of biogenic CO₂ can be captured and net-negative emissions of −158 to −510 ktonnes of CO₂ are potentially achieved by implementing carbon capture in the Gävle district heating system. Electricity production capacities in combined heat and power plants are significantly reduced, between 22% and 113% depending on the carbon capture process. Hot potassium-based processes generally reduce electricity generation more than processes based on amines or ammonia. The overall system effects strongly depend on the size and operational conditions of the plant equipped with carbon capture technology. Carbon capture in the Gävle district heating production system could potentially increase the local use of wood chips by as much as 44%. With the current European energy crisis in mind, the overall benefit of increasing biomass use for capturing CO₂ needs to be further scrutinized.