Economic models with global and economy-wide coverage can be useful tools to assess the impact of energy and environmental policies, but often disregard finer technological details of emission abatement measures. We present a framework for integrating and preserving detailed bottom-up information for end-of-pipe abatement technologies into a large-scale numerical model. Using an activity analysis approach, we capture non-linearities that typically characterise bottom-up abatement cost curves derived from discrete technology options. The model framework is flexible and can accommodate greenhouse gas and air pollution abatement, as well as modelling carbon capture and storage (CCS). Here, we illustrate this approach for non-CO2 greenhouse gases in a large-scale Computable General Equilibrium (CGE) model and compare results with a fitted marginal abatement curve and with completely excluding non-CO2 greenhouse gases. Results show that excluding non-CO2 abatement options leads to an overestimation of the total abatement cost. When the detailed bottom-up technology implementation is replaced by an estimated smooth marginal abatement cost curve, significant over- or underestimations of abatement levels and costs can emerge for particular pollutant-sector-region combinations.