We experimentally demonstrate tunable, phase-matched difference frequency generation covering the spectral region below 15 THz using 4H-SiC as a nonlinear crystal. This material combines a non-centrosymmetric lattice and strong birefringence with broadband transparency at low optical frequencies. Thorough refractive index measurements in the terahertz spectral range allow us to calculate phase-matching conditions for any near-infrared pump laser source. 4H-SiC is also exploited as a detector crystal for electro-optic sampling. The results allow us to estimate the effective second-order nonlinear coefficient.