Users are increasingly turning to online services, but are concerned for the safety of their personal data and critical business tasks. While secure communication protocols like TLS authenticate and protect connections to these services, they cannot guarantee the correctness of the endpoint system. Users would like assurance that all the remote data they receive is from systems that satisfy the users' integrity requirements. Hardware-based integrity measurement (IM) protocols have long promised such guarantees, but have failed to deliver them in practice. Their reliance on non-performant devices to generate timely attestations and ad hoc measurement frameworks limits the efficiency and completeness of remote integrity verification. In this paper, we introduce the integrity verification proxy (IVP), a service that enforces integrity requirements over connections to remote systems. The IVP monitors changes to the unmodified system and immediately terminates connections to clients whose specific integrity requirements are not satisfied while eliminating the attestation reporting bottleneck imposed by current IM protocols. We implemented a proof-of-concept IVP that detects several classes of integrity violations on a Linux KVM system, while imposing less than 1.5% overhead on two application benchmarks and no more than 8% on I/O-bound micro-benchmarks.