In ZK-Rollups, provers spend significant computational resources to generate validity proofs. Their costs should be compensated properly, so a sustainable prover market can form over time. Existing transaction fee mechanisms (TFMs) such as EIP-1559, however, do not work in this setting, as EIP-1559 only generates negligible revenue because of burning, while provers often create or purchase specialized hardware in hopes of creating long-term revenue from proving, somewhat reminiscent of proof-of-work miners in the case of chains like Bitcoin. In this paper, we explore the design of transaction fee mechanisms for prover markets. The desiderata for such mechanisms include efficiency (social welfare is maximized), incentive compatibility (it is rational to bid honestly), collusion resistance (no profitable collusion among provers exists), and off-chain agreement proofness (no profitable collusion between users and provers exists). To demonstrate the difficulties of our new setting, we put forward several simple strawman mechanisms, and show they suffer from notable deficiencies.