Fine particulate matter (PM2.5) and surface ozone (O3) are major air pollutants in megacities such as Delhi, but the design of suitable mitigation strategies is challenging. Some strategies for reducing PM2.5 may have the notable side effect of increasing O3. Here, we demonstrate a numerical framework for investigating the impacts of mitigation strategies on both PM2.5 and O3 in Delhi. We use Gaussian process emulation to generate a computationally efficient surrogate for a regional air quality model (WRFChem). This allows us to perform global sensitivity analysis to identify the major sources of air pollution and to generate emission-sector-based pollutant response surfaces to inform mitigation policy development. Based on more than 100 000 emulation runs during the pre-monsoon period (peak O3 season), our global sensitivity analysis shows that local traffic emissions from the Delhi city region and regional transport of pollution emitted from the National Capital Region (NCR) surrounding Delhi are dominant factors influencing PM2.5 and O3 in Delhi. They together govern the O3 peak and PM2.5 concentration during daytime. Regional transport contributes about 80% of the PM2.5 variation during the night. Reducing traffic emissions in Delhi alone (e.g. by 50 %) would reduce PM2.5 by 15 %–20 % but lead to a 20 %–25 % increase in O3. However, we show that reducing NCR regional emissions by 25 %–30 % at the same time would further reduce PM2.5 by 5 %–10 % in Delhi and avoid the O3 increase. This study provides scientific evidence to support the need for joint coordination of controls on local and regional scales to achieve effective reduction in PM2.5 whilst minimising the risk of O3 increase in Delhi.