Recently the study of layered human tissues in the presence of electromagnetic radiation has gained a lot of attention, in order to develop low-cost and efficient methods of health monitoring. In this work, we explore the electromagnetic field response of a layered air-skin-abdominal fat-muscle system both analytically and through simulation, and propose the use deep neural networks to make a non-invasive estimation of fat thickness. First, we explore the TM planewave response of the layered system with varying abdominal fat thickness, and results show that the location of resonance (minimum reflection) shifts towards the lower frequencies with increasing fat thickness. Then, we explore the TM Ez field response of a horizontal dipole and the S11 parameters of a wideband patch antenna over the same layered system. For both cases, we note that the presence of resonance is obscure; although there remains a distinct relation between the received fields magnitude and fat thickness. Taking these relations into account, we train a deep learning model to solve the inverse problem of estimating the abdominal fat thickness from those data. For both sources, the overall estimation accuracy was very high, with maximum estimation error being < 10%.