Simulating organic agriculture is a considerable challenge. One reason is that few models are capable of simulating crop-pest interactions and the yield losses they cause. Here, a recently developed process-based crop-pest model (Pest-EPIC) was used to simulate conventional and organic agriculture in the European Union for the years 1995–2100. Yields and pesticide application rates were calibrated against FAOSTAT and Eurostat data. Results indicate that current pesticide application rates may be sufficient to control pests and diseases even at the end of the century. The range of simulated yield differences under organic and conventional agriculture under current conditions (e.g., wheat 21–55% (mean 34%) lower yields; potatoes 20–99% (mean 56%) lower yields) closely matched recorded values. Under climate change, the gap between yields under conventional and organic management will remain constant for some crops (e.g., at 3 t/ha for potatoes), but others—susceptible to a larger number of pests and diseases—may experience a widening of the yield gap (e.g., increase of yield difference from 0.8 to 1.6 t/ha for wheat). The presented results-dataset may in future be a valuable resource for integrated assessments of agricultural land use and policy planning, but the inherent uncertainty is still very high.