The past few years have been very eventful with respect to the evolution of the concept and implementation of “left-handed materials (LHMs)”. This paper elucidates antenna parameter optimization using 2 Segment Labyrinth metamaterial embedded in antenna substrate at high frequency (THz). Ansoft HFSS has been used to design and analyse the RMPA (rectangular microstrip patch antenna) with design frequency 9.55 THz and operating range of 8.55 THz to 10.55 THz having RT Duroid (ε_r = 2.33) as substrate material. Magnetic properties of labyrinth resonator have been used to mathematically demonstrate the negative refraction. Nicolson Ross Wier (NRW) method has been used to retrieve the material parameters from transmission and reflection coefficient. Upon incorporation, bandwidth widens to around 4% and VSWR improves by approx 1.5%.