Metamemory involves the ability to correctly judge the accuracy of our memories. The retrieval of memories can be improved using transcranial electrical stimulation (tES) during sleep, but evidence for improvements to metamemory sensitivity is limited. Applying tES can enhance sleep-dependent memory consolidation, which along with metamemory requires the coordination of activity across distributed neural systems, suggesting that examining functional connectivity is important for understanding these processes. Nevertheless, little research has examined how functional connectivity modulations relate to overnight changes in metamemory sensitivity. Here, we developed a closed-loop short-duration tES method, time-locked to up-states of ongoing slow-wave oscillations, to cue specific memory replays in humans. We measured electroencephalographic (EEG) coherence changes following stimulation pulses, and characterized network alterations with graph theoretic metrics. Using machine learning techniques, we show that pulsed tES elicited network changes in multiple frequency bands, including increased connectivity in the theta band and increased efficiency in the spindle band. Additionally, stimulation-induced changes in beta-band path length were predictive of overnight changes in metamemory sensitivity. These findings add new insights into the growing literature investigating increases in memory performance through brain stimulation during sleep, and highlight the importance of examining functional connectivity to explain its effects.