Pressure testing systems comprise a clamp assembly for clamping a device for testing with a test fluid, and a control assembly for controlling application of a clamp pressure to the device. The control assembly comprises a clamp control structure with an activated configuration and an inactivated configuration. In the activated configuration, the clamp control structure permits the clamp pressure to be applied to the device. In the inactivated configuration, the clamp control structure permits the clamp pressure to be released from the device. The control assembly also comprises a safety structure that is actuated by the test fluid between an interlocked configuration and a disengaged configuration. In the interlocked configuration, the safety structure physically prevents the clamp control structure from reconfiguring from the activated configuration to the inactivated configuration. In the disengaged configuration, the safety structure permits the clamp control structure to be reconfigured from the activated configuration to the inactivated configuration.