Modern ransomware often generate and manage cryptographic keys on the victim's machine, giving defenders an opportunity to capture exposed keys and recover encrypted data without paying the ransom. However, recent work has raised the possibility of future enclave-enhanced malware that could avoid such mitigations using emerging support for hardware-enforced secure enclaves in commodity CPUs. Nonetheless, the practicality of such enclave-enhanced malware and its potential impact on all phases of the ransomware lifecyle remain unclear. Given the demonstrated capacity of ransomware authors to innovate in order to better extort their victims (e.g. through the adoption of untraceable virtual currencies and anonymity networks), it is important to better understand the risks involved and identify potential mitigations. As a basis for comprehensive security and performance analysis of enclave-enhanced ransomware, we present RansomClave, a family of ransomware that securely manage their cryptographic keys using an enclave. We use RansomClave to explore the implications of enclave-enhanced ransomware for the key generation, encryption and key release phases of the ransomware lifecycle, and to identify potential limitations and mitigations. We propose two plausible victim models and analyse, from an attacker's perspective, how RansomClave can protect cryptographic keys from each type of victim. We find that some existing mitigations are likely to be effective during the key generation and encryption phases, but that RansomClave enables new trustless key release schemes that could potentially improve attacker's profitability and, by extension, make enclaves an attractive target for future attackers.