Designing autonomous systems that can adapt safely remains an open problem in robotics, mainly due to uncertain and dynamic environmental conditions that can render these systems uncontrollable. An important aspect for building safe adaptation is to identify states where system adaptation can occur safely. This is captured by the concept of quiescence. Assuring quiescence requires an infrastructure capable of monitoring and managing the state of the adapted system, thereby guaranteeing system consistency throughout the adaptation process. However, such an infrastructure has not yet been realized for robotic systems. To fill this research gap, we present a framework, called AMAR, for ensuring correct system behavior during the adaptation of multi-robot systems. Focusing at runtime, we execute the robotic mission and monitor the state of the system to determine when an adaptation should occur. The results of the evaluation show that AMAR reliably enforces safety properties and that its quiescence monitors are highly accurate.