Despite our best efforts, any sufficiently complex computer system has vulnerabilities. It is safe to assume that such vulnerabilities can be exploited by attackers who will be able to penetrate the system. Intrusion tolerance attempts to maintain acceptable service despite such intrusions. This paper presents an application of intrusion-tolerance concepts to Enclaves, a software infrastructure for supporting secure group applications. Intrusion tolerance is achieved via a combination of Byzantine fault-tolerant protocols and secret sharing techniques.