For low-Earth-orbit (LEO) satellites, high-precision clock estimation often depends on high-precision real-time global navigation satellite system (GNSS) products. Thus, service providers often choose to downlink observation data to the ground to achieve high accuracy. To relieve this burden for future LEO mega-constellations, this study investigates the performance of relative clocks and orbits determined between LEO satellites using the phase common-view (PCV) method. The PCV results are compared with results from three other single-satellite-based clock and orbit determination methods. Using real data from the Gravity Recovery and Climate Experiment (GRACE) Follow-On satellites and three different types of real-time GNSS products, the PCV method can deliver a relative clock precision below 0.2 ns and a relative orbital user range error of approximately 5 cm, even when using the broadcast ephemeris, whereas all three other methods encountered sharp degradations in their results when using degraded real-time GNSS products.