This paper studies model-based input-output conformance testing in the presence of queues. Normally, it is assumed that a test case communicates synchronously with an implementation under test. This causes some challenges in practice, since testing is often conducted asynchronously. In an asynchronous environment messages between a tester and the implementation are queued. This may lead to incorrect verdicts. In this paper we show how one can guarantee correct verdicts in the asynchronous case for a large set of implementations. If choices between inputs and outputs are restricted to internal choices with respect to an implementation one can use the observation of quiescence as a handshake between a test case and the implementation. Such a handshake allows us to test for input-output conformance in the context of queues. In addition, the input-enabledness assumption on implementations is relaxed. Besides a formal discussion of this approach, we show the practical relevance by applying our approach to a conference protocol.