Model-based reconstruction is an approach to infer network structures where they cannot be observed. For archaeological networks, several models based on assumptions concerning distance among sites, site size, or costs and benefits have been proposed to infer missing ties. Since these assumptions are formulated at a dyadic level, they do not provide means to express dependencies among ties and therefore include less plausible network scenarios. In this paper we investigate the use of network models that explicitly incorporate tie dependence. In particular, we consider exponential random graph models, and show how they can be applied to reconstruct networks coherent with Burt's arguments on closure and structural holes (Burt 2001). The approach is illustrated on data from the Middle Bronze Age in the Aegean.