In this work the basin of stability of synchronized states in a system of two mutually delay-coupled phase-locked loops (PLLs) is studied. For sufficiently large cross-coupling time delays several synchronized states with different frequencies and phase relations can exist. This is termed multistability. Using PLL nodes with voltage-controlled oscillators operating at 24 GHz the basin of stability of in- and anti-phase synchronized states is measured. The PLL nodes were modified accordingly to measure the transient dynamics during synchronization. A comparison to the results of time domain simulations of the transient dynamics reveals that such dynamics can be predicted qualitatively and quantitatively. Based on these results, a deeper understanding of the synchronization process at time delays resulting in multistable states in coupled PLL networks, can be obtained.