This article presents terahertz time-domain spectroscopy methods to measure optical characteristics up to about 3 THz and characterize the complex dielectric function in the long-wave infrared spectrum for ultrahigh mobility HgCdTe films. The Drude-Lorentz model is fit to complex transmission function measurements, and the Kane model is used to describe the band structure of the films for the dielectric characterization. These techniques are useful to accurately describe temperature-dependent conduction band carrier density, carrier mobility, effective mass and scattering time at temperatures below 100°K for ultrahigh mobilities greater than 105cm^2/v/s and ionized donor densities less than 3x10^15/cm3.