Given limited network information, we consider robust risk quantification under the Eisenberg-Noe model for financial networks. To be more specific, motivated by the fact that the structure of the interbank network is not completely known in practice, we propose a robust optimization approach to obtain worst-case default probabilities and associated capital requirements for a specific group of banks (e.g., systemically important financial institutions) under network information uncertainty. Using this tool, we analyze the effects of various incomplete network information structures on these worst-case quantities and provide regulatory insights into the collection of actionable network information. All claims are numerically illustrated using data from the European banking system.