Many websites provide restrictive form-like interfaces which allow users to execute search queries on the underlying hidden databases. In this paper, we consider the problem of estimating the size of a hidden database through its web interface. We propose novel techniques which use a small number of queries to produce unbiased estimates with small variance. These techniques can also be used for approximate query processing over hidden databases. We present theoretical analysis and extensive experiments to illustrate the effectiveness of our approach. Categories and Subject Descriptors H.2.7 [Database Administration]; H.3.5 [Online Information Services]: Web-based services General Terms Algorithms, Measurement, Performance Keywords Hidden Databases, Aggregate Query Processing