Atmospheric methane directly affects surface temperatures and indirectly affects ozone, impacting human welfare, the economy, and environment. The social cost of methane (SC-CH4) metric estimates the costs associated with an additional marginal metric ton of emissions. Current SC-CH4 estimates do not consider the indirect impacts associated with ozone production from changes in methane. We use global model simulations and a new BenMAP webtool to estimate respiratory-related deaths associated with increases in ozone from a pulse of methane emissions in 2020. By using an approach consistent with the current SC-CH4 framework, we monetize and discount annual damages back to present day values. We estimate that the methane-ozone mechanism is attributable to 760 (95% CI: 330-1200) respiratory-related deaths per million metric tons of methane globally, for a global net present damage of $1800/mT (95% CI: $760-$2800/Mt CH4; 2% Ramsey discount rate); this would double the current SC-CH4 if included. These physical impacts are consistent with recent studies, but comparing direct costs is challenging. Economic damages are sensitive to uncertainties in the exposure and health risks associated with tropospheric ozone, assumptions about future projections of NOx emissions, socioeconomic conditions, and mortality rates, monetization parameters, and other factors. Our estimates are highly sensitive to uncertainties in ozone health risks. We also develop a reduced form model to test sensitivities to other parameters. The reduced form tool runs with a user-supplied emissions pulse, as well as socioeconomic and precursor projections, enabling future integration of the methane-ozone mechanism into the SC-CH4 modeling framework.