Today, wearable systems are facing fundamental barriers in terms of battery lifetime and quality of their results. The main challenge in wearable systems is to increase the battery lifetime, while maintaining the machine-learning performance of the system. A recently proposed concept for overcoming this challenge is self-awareness, which increases system's knowledge of itself and the surrounding environment. This is precisely what health monitoring wearable systems require to adapt to different situations. To demonstrate the impact of introducing self-awareness in wearable technologies, we consider the epileptic seizure detection problem, as a case study. Epilepsy affects around 1% of the world's population, which can dramatically degrade the quality of life and represents a major public health issue. As a result, detection of epileptic seizures has become more important over the past decades. In this paper, we aim to introduce a new generation of self-aware wearable systems to decrease energy consumption and improve their seizures detection capabilities by introducing the notion of self-awareness in such systems. These techniques include switching to low-power mode to reduce the energy consumption and machine-learning model enhancement to improve detection quality. We incorporated our proposed techniques in the machine learning module, which detects epileptic seizures by monitoring the cardiac and respiratory systems. We evaluated the performance of our approach based on an epilepsy database of more than 141 hours, provided by the Lausanne University Hospital (CHUV). Our self-aware wearable system achieves 36% reduction in computational complexity and 10.51% improvement in detection performance.