We have developed a method to characterize the spectral response of an uncooled microbolometer focal plane array at a broad range of terahertz (THz) frequencies (4~50 THz). This is achieved by using a spectrum-tailored blackbody radiator as a broadband THz source and measuring its spectral power with a Fourier transform infrared (FTIR) interferometer. With an additional measurement with a pyroelectric detector as a reference, the spectral response of the microbolometer relative to the pyroelectric reference is obtained with a signal-to-noise ratio of 100 over a >50 THz bandwidth.