Higher-order transverse electric and transverse magnetic modes in gigahertz transverse electromagnetic cells are investigated using the mode-matching method. The gigahertz transverse electromagnetic cell is modeled as a right rectangular pyramid with a thin septum. Fields are expanded in eigenfunctions of spherical coordinates, and the orthogonality of sinusoidal functions is utilized to obtain simple modal equations. Computations are performed to check the accuracy and convergence of modal series solutions. The characteristics of modal series solutions are presented in terms of gigahertz transverse electromagnetic cell geometries.