Connected Autonomous Vehicles have great potential to improve automobile safety and traffic flow, especially in cooperative applications where perception data is shared between vehicles. However, this cooperation must be secured from malicious intent and unintentional errors that could cause accidents. Previous works typically address singular security or reliability issues for cooperative driving in specific scenarios rather than the set of errors together. In this paper, we propose CONClave, a tightly coupled authentication, consensus, and trust scoring mechanism that provides comprehensive security and reliability for cooperative perception in autonomous vehicles. CONClave benefits from the pipelined nature of the steps such that faults can be detected significantly faster and with less compute. Overall, CONClave shows huge promise in preventing security flaws, detecting even relatively minor sensing faults, and increasing the robustness and accuracy of cooperative perception in CAVs while adding minimal overhead.