Wireless-connected wearable electronics are finding extensive usage for diagnostic and therapeutic purposes after the globally spread pandemic disease of COVID-19. Although they are undoubtedly helpful for keeping physical distance, their health effects are still under investigation from different aspects and are still a concern for the end-users. In this study, a custom M-shaped wearable antenna covering the wireless body area network and wireless local area network frequencies is designed, built, and measured. A beret cap made from a 2 mm thick textile is used as a substrate. The specific absorption rate (SAR) in a realistic human-head model due to electromagnetic energy produced by the antenna is evaluated using the finite-difference time-domain method. The SAR distributions for 1-g and 10-g tissues are calculated at 2.4 and 5.8 GHz. It is shown that the obtained maximum SAR values for 1-g and 10-g tissues at each frequency of interest were less than the limits determined by IEEE RF exposure guidelines and standards.