In recent years, high-precision Low Earth Orbit (LEO) satellite orbital and clock errors have been studied for augmenting the Global Navigation Satellite System (GNSS)-based positioning, navigation and timing services. Compared to the orbital and clock products separately, the accuracy of the combined orbital and clock errors projected on the Earth, i.e., the Signal-In-Space Range Error (SISRE), are of higher concern for ground users. This study used real data from GRACE Follow-on satellites flying at about 500 km, and processed the near-real-time LEO satellite orbits and clocks in the reduced-dynamic and kinematic modes with a batch least-squares adjustment using real-time GNSS products provided by the French National Centre for Space Studies (CNES). Results showed that the orbital user range error amounts to about 1–2 cm in the reduced-dynamic mode, and about 2–3 cm in the kinematic mode. The precision of the clock errors reaches about 0.1 ns for both processing modes and both satellites. The SISREs of both tested GRACE Follow-on satellites amount to about 3.5–4 cm, for both the reduced-dynamic and kinematic modes.