Free-space time domain THz spectroscopy accesses material electrodynamic responses in a frequency regime ideally matched to interacting condensed matter energy scales. THz spectroscopy, however, is challenging when samples are physically smaller than the diffraction limit of ~0.5 mm, as is typical, for example, in van der Waals materials and heterostructures. We examine engineering considerations at THz frequencies, present an on-chip, time-domain THz spectrometer with a bandwidth of 750 GHz, and extract the optical conductivity of a 7.5-um wide NbN film across the superconducting transition. Our spectrometer’s interchangeable sample architecture makes it ideal for probing superconductivity, magnetism, and charge order in strongly correlated van der Waals materials.