We have demonstrated the viability of using the Laser Ranging Interferometer on the Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) space mission to test key aspects of the interspacecraft interferometry proposed for detecting gravitational waves. The Laser Ranging Interferometer on GRACE-FO will be the first demonstration of interspacecraft interferometry. GRACE-FO shares many similarities with proposed space-based gravitational wave detectors based on the Laser Interferometer Space Antenna (LISA) concept. Given these similarities, GRACE-FO provides a unique opportunity to test novel interspacecraft interferometry techniques that a LISA-like mission will use. The LISA Experience from GRACE-FO Optical Payload (LEGOP) is a project developing tests of arm locking and time delay interferometry (TDI), two frequency stabilization techniques, that could be performed on GRACE-FO. In the proposed LEGOP TDI demonstration one GRACE-FO spacecraft will have a free-running laser while the laser on the other spacecraft will be locked to a cavity. It is proposed that two one-way interspacecraft phase measurements will be combined with an appropriate delay in order to produce a round-trip, dual one-way ranging (DOWR) measurement independent of the frequency noise of the free-running laser. This paper describes simulated and experimental tests of a tone-assisted TDI ranging (TDIR) technique that uses a least-squares fitting algorithm and fractional-delay interpolation to find and implement the delays needed to form the DOWR TDI combination. The simulation verifies tone-assisted TDIR works under GRACE-FO conditions. Using simulated GRACE-FO signals the tone-assisted TDIR algorithm estimates the time-varying interspacecraft range with a rms error of $\ifmmode\pm\else\textpm\fi{}0.2\text{ }\text{ }\mathrm{m}$, suppressing the free-running laser frequency noise by 8 orders of magnitude. The experimental results demonstrate the practicability of the technique, measuring the delay at the 6 ns level in the presence of a significant displacement signal.