Secondary glazing is an effective way to enhance the thermal performance and energy efficiency of heritage buildings without compromising their historical and architectural significance. While cost-effective over time, the upfront expense can be substantial. Alternatively, replacing the original single glazing with thin, high-performance double glazing may be considered. This study examines the thermal performance of adding secondary glazing versus replacing the original single glazing by advanced double glazing in the original frame of a common Dutch sash heritage window. Detailed 3D-thermal simulations that account for heat transfer by radiation in the cavity are used to compare the different renovation measures. These simulations however do not account for air in- and exfiltration. Bearing in mind the poor airtightness of common heritage windows, the thermal simulations are complemented by a simple hand calculation to estimate additional heat losses due to airflow. Findings show that heat losses from poor airtightness are comparable to losses from conduction. Therefore, installing airtight secondary glazing, even with modest thermal performance, is more effective than replacing single glazing with high-performing alternatives.