Data Stream Management (DSM) addresses the continuous processing of sensor data. DSM requires the combination of stream operators, which may run on different distributed devices, into stream processes. Due to the recent advantages in sensor technologies and wireless communication, DSM is increasingly gaining importance in various application domains. Especially in healthcare, the continuous monitoring of patients at home (telemonitoring) can significantly benefit from DSM. A vital requirement in telemonitoring is however that DSM provides a high degree of reliability. In this paper, we present a novel approach to efficient and coordinated stream operator checkpointing supporting reliable DSM while maintaining the high result quality needed for healthcare applications. Furthermore, we present evaluation results of our checkpointing approach implemented within our process and data stream management infrastructure OSIRIS-SE. OSIRIS-SE supports flexible failure handling and efficient and coordinated checkpointing by means of consistent operator migration. This ensures complete and consistent continuous data stream processing even in the case of failures.