Motivated by our eight-year partnership with a local food bank, we present two robust optimization models to support the equitable and effective distribution of donated food over the food bank's service area. Our first model addresses uncertainty in the amount of donated food counties can effectively receive and distribute, which depends on local factors such as budget and workforce that are unknown to the food bank. Assuming that the capacity of each county varies within a range, the model seeks to maximize total food distribution while enforcing a user-specified level of robustness. Our second model uses robust optimization in a nontraditional manner, treating the upper bound on the level of allowed inequity as an uncertain parameter and limiting total deviation from a perfectly equitable distribution over all counties while maximizing total food shipment. We derive structural properties of both models and develop efficient exact solution algorithms. We illustrate our models using historical data obtained from our food bank partner, summarize the policy implications of our results and examine the impact of uncertainty on outcomes and decision making.