While the current network protocols and systems become more and more complex, the testing process of their functional and non-functional behaviors comes to be crucial. Among the testing techniques, we herein focus on their test at runtime in an online way which requires the ability to handle numerous messages in a short time with the same offline testing preciseness. Meanwhile, since online testing is a long term continuously process, the tester has to undergo severe conditions when dealing with large amount of nonstop traces. In this paper, we present a novel logic-based online passive testing approach to test, at runtime, the protocol conformance and performance through formally specified properties with new definitions of verdicts. Furthermore, we experimented our approach with several Session Initiation Protocol (SIP) properties in a real IP Multimedia Subsystem environment and obtained relevant verdicts