The work reported in this thesis is motivated by the need for wireless powering of a miniaturized implantable device for neurophysiological research and possible clinical applications. The antenna used in such applications must be studied in the context of biological tissue media. In this thesis, we perform a preliminary study of antenna behaviour in the complex tissue environment. Our test cases are the wire dipole antenna chosen for its structural simplicity and the spiral antenna, selected for its wide bandwidth. The simulation tool SEMCAD-X, is based on the Finite-Difference Time-Domain (FDTD) method and is used throughout this work. To have an in-depth understanding of the characteristics of different solvers implemented in SEMCAD-X and relevant for our applications, we first simulate the antenna structures in the free-space region using both SEMCAD-X and HFSS (a Finite-Element Method (FEM) simulation software). The cross-platform comparison between these two simulation tools helps us identify the advantages of using conformal FDTD solver over the conventional staircase FDTD solver in SEMCAD-X. We then embed the antennas in tissue-like non-homogeneous lossy media to observe the terminal voltages induced by an impinging plane-wave. These numerical experiments will help us with the assessment of the following: variations of antenna properties with the in-tissue locations, and more importantly the dependence of the induced voltage on the depth of the implant.