We study methods to enhance privacy in blockchain transactions from an economic angle. We consider mechanisms for privacy-aware users whose utility depends not only on the outcome of the mechanism but also negatively on the exposure of their economic preferences. Specifically, we study two auction-theoretic settings with privacy-aware users. First, we analyze an order flow auction, where a user auctions off to specialized agents, called searchers, the right to execute her transaction while maintaining a degree of privacy. We examine how the degree of privacy affects the revenue of the auction and, broadly, the net utility of the privacy-aware user. In this new setting, we describe the optimal auction, which is a sealed-bid auction. Subsequently, we analyze a variant of a Dutch auction in which the user gradually decreases the degree of privacy until the transaction is sold. We compare the revenue of this auction to that of the optimal one as a function of the number of auction rounds. Then, we introduce a two-sided market - a privacy marketplace - with multiple users selling their transactions under their privacy preferences to multiple searchers. We design a posted-price mechanism for the two-sided market that guarantees constant approximation of the optimal social welfare while maintaining incentive compatibility (from both sides of the market) and budget balance. This work builds on the emerging line of research that attempts to improve the performance of economic mechanisms by appending cryptographic primitives to them.