Designing antennas for implanted medical devices is a very complex task where one needs to tackle inherently large EM absorption in the human tissue and very limited available space for the antenna. In addition, designers need to carefully limit the power output of the devices due to health safety regulations and small battery volume. Furthermore, the initial designs assume that permittivity and conductivity of different types of human tissues are known. Unfortunately, these values have a significant variation depending on the age, sex and health conditions of the actual patient. Such variations need to be taken into account in initial designs and in this paper we analyze the influence which the uncertainty of the tissues dielectric parameters have on the predictable power density in implanted antenna scenarios.