We present a series of simulations to demonstrate that high-fidelity velocity-delay maps of the emission-line regions in active galactic nuclei (AGNs) can be obtained from time-resolved spectrophotometric data sets like those that will arise from the proposed Kronos satellite. While previous reverberation-mapping experiments have established the size scale R of the broad emission-line regions from the mean time delay τ=R/c between the line and continuum variations and have provided strong evidence for supermassive black holes, the detailed structure and kinematics of the broad-line region remain ambiguous and poorly constrained. Here we outline the technical improvements that will be required to successfully map broad-line regions by reverberation techniques. For typical AGN continuum light curves, characterized by power-law power spectra P(f)~f-α with α=-1.5+/-0.5, our simulations show that a small UV/optical spectrometer like Kronos will clearly distinguish between currently viable alternative kinematic models. From spectra sampled at time intervals ∆t and sustained for a total duration Tdur, we can reconstruct high-fidelity velocity-delay maps with velocity resolution comparable to that of the spectra, and delay resolution ∆τ~2∆t, provided that Tdur exceeds the broad-line region light crossing time by at least a factor of 3. Even very complicated kinematical models, such as a Keplerian flow with superimposed spiral wave pattern, are resolved in maps from our simulated Kronos data sets. Reverberation mapping with Kronos data is therefore likely to deliver the first clear maps of the geometry and kinematics in the broad emission-line regions 1-100 μas from supermassive black holes.