In this paper we pursue three main objectives: (1) to develop a model of an intermediated search market in which matching between consumers and firms takes place primarily via paid referrals; (2) to address the question of designing a suitable mechanism for selling referrals to firms; and (3) to characterize and analyze the firms’ bidding strategies given consumers’ equilibrium search behavior. To achieve these objectives we develop a two-stage model of search intermediaries in a vertically differentiated product market. In the first stage an intermediary chooses a search engine design that specifies to which extent a firm’s search rank is determined by its bid and to which extent it is determined by the product offering’s performance. In the second stage, based on the search engine design, competing firms place their open bids to be paid for each referral by the search engine. We find that the revenue-maximizing search engine design bases rankings on a weighted average of product performance and bid amount. Nonzero pure-strategy equilibria of the underlying discontinuous bidding game generally exist but are not robust with respect to noisy clicks in the system. We determine a unique nondegenerate mixed-strategy Nash equilibrium that is robust to noisy clicks. In this equilibrium firms of low product performance fully dissipate their rents, which are appropriated by the search intermediary and the firm with the better product. The firms’ expected bid amounts are generally nonmonotonic in product performance and depend on the search engine design parameter. The intermediary’s profit-maximizing design choice, by attributing a positive weight to the firms’ bids, tends to obfuscate search results and reduce overall consumer surplus compared to the socially optimal design of fully transparent results ranked purely on product performance.