To achieve the future demand of high data rates and high gain with better efficiency, two nano Microstrip patch antennas were designed with nickel and silver substrates. The operating or resonance frequency selected for the two antennas was 0.25 THz or 250 GHz. The main reason behind designing the antenna at 250 GHz is that the frequency range is completely free. The rectangular shape of the patch was selected because of the simplicity of dimension calculation. The transmission line model was taken for the analytical purpose. It is the simplest model of all other models. The values of patch width and length were calculated. The height of the antenna was taken too small for better performance. To operate the antennas at desired 250 GHz some dimensions were varied. Directivity of 16.37 dBi was found for the Nickel substrate patch antenna and 17.37 dBi directivity was found for the Silver substrate patch antenna.