Increased system robustness is one of the promises of modularity. However, research on the topic has provided conflicting findings. By generating more than 2000 system architectures, this paper shows that the relation between modularity and robustness is multifaceted: Modularity decreases topological robustness, increases robustness to change propagation, and provides economic benefits. Results here confirm the importance of modularity, enable reconciliation of opposing findings from prior research, and guides researchers and practitioners in the selection of appropriate robustness measures.