This thesis reports on a periodic Finite-Difference Time-Domain methodology for the analysis of loaded Transmission-Line Negative-Refractive-Index metamaterials. The modular unit cell of this periodic structure is simulated using the Finite-Difference Time-Domain technique and the computational domain is terminated with periodic boundary conditions. The proposed methodology is applied to the accurate and efficient dispersion analysis of the aforementioned structure and the calculation of the field patterns of the major supported modes. In turn, this methodology is properly extended in order to be employed for the full-wave analysis of Negative-Refractive-Index metamaterial-based leaky-wave antennas and the extraction of their radiation patterns, in a much more numerically efficient way than previously reported approaches.