The global overexploitation of fish stocks is endangering many marine food webs. Scientists and managers now call for an ecosystem-based fisheries management, able to take into account the complexity of marine ecosystems and the multiple ecosystem services they provide. By contrast, many fishery management plans only focus on maximizing the productivity of harvested stocks. Such practices are suggested to affect other ecosystem services, altering the integrity and resilience of natural communities. Here we show that while yield-maximizing policies can allow for coexistence and resilience in predator–prey communities, they are not optimal in a multi-objective context. We find that although total prey and predator maximum yields are higher with a prey-oriented harvest, focusing on the predator improves species coexistence. Also, moderate harvesting of the predator can enhance resilience. Furthermore, increasing maximum yields by changing catchabilities improves resilience in predator-oriented systems, but reduces it in prey-oriented systems. In a multi-objective context, optimal harvesting strategies involve a general tradeoff between yield and resilience. Resilience-maximizing strategies are however compatible with quite high yields, and should often be favored. Our results further suggest that balancing harvest between trophic levels is often best at maintaining simultaneously species coexistence, resilience and yield.