Pollution from past industrial activities can remain unnoticed for years or even decades because the pollutant has only recently gained attention or been identified by measurements. Modeling the emission history of pollution is essential for estimating population exposure and apportioning potential liability among stakeholders. This paper proposes a novel approach for reconstructing the history of polychlorinated dibenzo-p-dioxin (PCDD) and polychlorinated dibenzofuran (PCDF) pollution from municipal solid waste incinerators (MSWIs) with unknown past emissions. The proposed methodology relies on the search for technical and operational data on the pollution source in archives, the extraction of representative data from the scientific literature, and the use of kinetic models of the formation and decomposition of PCDD/Fs within combustion chambers. This new methodological tool allows to estimate any MSWI's stack emission and relative profile of seventeen PCDD/F congeners over time. The approach is validated through a case study of an MSWI in Switzerland. The modeled congener profile achieved a Pearson correlation coefficient of 0.98 with measurements in fly ash washwater. Additionally, the simulated soil quantity (1,115-1,419 gTEQ WHO-2005 or 1,283-1,698 gTEQ WHO-2022) agrees in order of magnitude with the estimated quantity from measurements (371 gTEQ WHO-2005 or 425 gTEQ WHO-2022).