This paper seeks to fill a gap in existing computational models of the production of referring expressions, by addressing situations in which speakers have difficulty assessing what information is available to their audience. The paper describes a two-part experiment where speakers were given the name of a famous person and had to create a description that would enable a hearer to identify the person, and hearers used the created descriptions to guess the name of the described person. The experiment compares how confident hearers are that they have identified the referent and how well speakers can estimate this confidence. The results of the experiment suggest that speakers do not overestimate hearers' confidence as the psycholinguistic literature had led us to expect.