Earthquake swarms, typically modeled as time‐varying changes in background seismicity, which are driven by external processes such as fluid flow or aseismic creep, present challenges for operational earthquake forecasting. Although the time decay of aftershock sequences can be estimated with the modified Omori law, it is difficult to forecast the temporal behavior of seismicity rates during a swarm. To explore these issues, we apply the epidemic‐type aftershock sequence (ETAS) model (Ogata, 1988) to the 2015 San Ramon, California swarm, which lasted several weeks and had almost 100 earthquakes. We develop three‐day forecasts during the swarm based on an ETAS model fit to all prior seismicity in the region as well as an ETAS model fit only to previous swarms in the region, which is better at capturing the higher background rate during the swarm. We also explore forecasts in which the background rate is updated periodically during the swarm using data over different lookback windows and find generally these models perform better than the models in which the background rate is fixed. Finally, we construct ensemble forecasts by combining the different models weighted according to their performance. The ensemble forecasts outperform all of the individual models and allow us to avoid making arbitrary choices at the outset of a swarm as to which single model will perform the best.