The clandestine nature of covert networks makes reliable data difficult to obtain and leads to concerns with missing data. We explore the use of network models to represent missingness mechanisms. Exponential random graph models provide a flexible way of parameterising departures from conventional missingness assumptions and data management practices. We demonstrate the effects of model specification, true network structure, and different not-at-random missingness mechanisms across six empirical covert networks. Our framework for modelling realistic missingness mechanisms investigates potential inferential pitfalls, evaluates decisions in collecting data, and offers the opportunity to incorporate non-random missingness into the estimation of network generating mechanisms.