Methods for increasing the bandwidth of time‐domain‐reflectometry (TDR) dielectric spectroscopy using variable‐time‐scale sampling are presented. Consecutive segments of the TDR transient are sampled with increasing time increments and the entire transient transformed into the frequency domain using a running Laplace transform. Instrumentation artifacts are identified and controlled by examining reflected transients for stray artifacts prior to transformation, either on individual time scales or on a composite log time scale. Transform algorithms are verified usingspicesimulation in both time and frequency domains. Results are presented for a conducting salt solution, showing continuous dielectric spectra from 100 kHz to 5 GHz in the frequency domain, and requiring acquisition over six decades of time in the time domain to capture the entire response.