In this article, we propose three-dimensional antenna systems for determining the position of electromagnetic radiation source at an unknown location. Received signal power at different antennas and position of radiation source are used as training data for Artificial Neural Network (ANN). It is found that, a well-trained ANN is computationally efficient and capable of predicting the unknown location of the source, from the received power pattern. Two multi-antenna systems with geometry in three dimensions, namely the cube and frustum, are considered in this paper. Further, test results of the proposed method for random positions of electromagnetic source, spanning a hemisphere, are presented for the geometries considered.