Because it is sensitive to fluctuations occurring over femtoseconds to picoseconds, gigahertz-to-terahertz dielectric relaxation spectroscopy can provide a valuable window into water's most rapid intermolecular motions. In response, we have built a vector network analyzer dielectric spectrometer capable of measuring absorbance and index of refraction in this frequency regime with unprecedented precision. Using this to determine the complex dielectric response of water and aqueous salt solutions from 5.9 GHz to 1.12 THz (which we provide in the supplementary material), we have obtained strong new constraints on theories of water's collective dynamics. For example, while the salt-dependencies we observe for water's two slower relaxations (8 and 1 ps) are easily reconciled with suggestions that they arise due to rotations of fully and partially hydrogen bonded molecules, respectively, the salt-dependence of the fastest relaxation (180 fs) appears difficult to reconcile with its prior assignment to liberations of single hydrogen bonds.