Electrical contacts provide a well-proven solution to switching various loads in a wide variety of applications, such as power distribution, control applications, automotive and telecommunications. However, electrical contacts are known for limited reliability due to degradation effects upon the switching contacts due to arcing and fretting. Essentially, the life of the device may be determined by the limited life of the contacts. Failure to trip, spurious tripping and contact welding can, in critical applications such as control systems for avionics and nuclear power application, cause significant costs due to downtime, as well as safety implications. Prognostics provides a way to assess the remaining useful life (RUL) of a component based on its current state of health and its anticipated future usage and operating conditions. In this thesis, the effects of contact wear on a set of electromagnetic relays used in an avionic power controller is examined, and how contact resistance combined with a prognostic approach, can be used to ascertain the RUL of the device. Two methodologies are presented, firstly a Physics based Model (PbM) of the degradation using the predicted material loss due to arc damage. Secondly a computationally efficient technique using posterior degradation data to form a state space model in real time via a Sliding Window Recursive Least Squares (SWRLS) algorithm. Health monitoring using the presented techniques can provide knowledge of impending failure in high reliability applications where the risks associated with loss-of-functionality are too high to endure. The future states of the systems has been estimated based on a Particle and Kalman-filter projection of the models via a Bayesian framework. Performance of the prognostication health management algorithm during the contacts life has been quantified using performance evaluation metrics. Model predictions have been correlated with experimental data. Prognostic metrics including Prognostic Horizon (PH), alpha-Lamda (α-λ), and Relative Accuracy have been used to assess the performance of the damage proxies and a comparison of the two models made.