Compared to conventional monoethanolamine (MEA), alternative solvents are expected to substantially contribute to reduce the energy demand of post-combustion CO2 capture from flue gases. This study presents a comprehensive techno-economic analysis of a 27 wt% 2-amino-2-methyl-1-propanol (AMP) + 13 wt% piperazine (PZ) aqueous solution for CO2 capture, compared to a 30 wt% MEA solution. The study addresses the retrofit of a carbon capture unit to a biomass-fired combined heat and power (CHP) plant, effectively making it a bioenergy with a carbon capture and storage (BECCS) system. The treated flue gas has a flow rate of 23 tons/hour (t/h) with 11.54 vol% CO2 and a 90% capture rate is aimed for. Aspen Plus V14 was employed for process simulations. Initially, binary interaction parameters for AMP/PZ, AMP/H2O, and PZ/H2O are regressed using vapor-liquid equilibrium (VLE) data, which were retrieved from literature along with reaction kinetics. Validation of parameters from available experimental literature yields an average absolute relative deviation (AARD) of only 5.9%. Afterwards, a process simulation model is developed and validated against experimental data from a reference pilot plant, using a similar AMP/PZ blend, resulting in 5% AARD. Next, a sensitivity analysis optimizes operating conditions, including solvent rate, absorber/stripper packing heights, and stripper pressure, based on regeneration energy impact. Optimized results, compared to MEA, reveal that AMP/PZ reduces the energy consumption from 3.61 to 2.86 GJ/tCO2. The retrofitting of the capture unit onto the selected CHP plant is examined through the development of a dedicated model. Two control strategies are compared to address energy unavailability for supplying the capture unit. The analysis spans 4 months, selected to account for seasonal variations. At nominal capacity, CO2 emissions, rendered negative by biomass combustion and CO2 capture, reach a maximum of −3.4 tCO2/h compared to 0.36 tCO2/h before retrofitting. Depending on the control strategy and CHP plant operating point, the Specific Primary Energy Consumption for CO2 Avoided (SPECCA) ranges from 4.91 MJ/kgCO2 to 1.76 MJ/kgCO2. Finally, an economic comparison based on systematic methodology reveals a 7.87% reduction in capture cost favoring the AMP/PZ blend. Together, these findings highlight AMP/PZ as a highly favorable alternative solvent.