Over the past decade, hyperscanning has emerged as an important methodology to study neural processes underlying human interaction using fMRI, EEG, fNIRS, and MEG. However, many methodological decisions regarding preprocessing and analysis of hyperscanning data have not yet been standardized in the hyperscanning community, yet may affect inter-brain estimates. Here we systematically investigate the effects common methodological choices can have on estimates of phase-based inter-brain synchronization (IBS) measures, using real and simulated hyperscanning (dual) EEG data. Notably, we introduce a new method to compute circular correlation (CCorr) coefficients in IBS studies, which performs more reliably in comparison to the standard approach, showing that the conventional CCorr implementation leads to large fluctuations in IBS estimates due to fluctuations in circular mean directions. Furthermore, we demonstrate how short epoch durations (of 1 second or less) can lead to inflated IBS estimates in scenarios with no strong underlying interaction. Finally, we show how signal-to-noise ratios and temporal factors may confound IBS estimates, particularly when comparing e.g., resting states with conditions involving motor actions. For each of these investigated effects, we provide recommendations for future research employing hyperscanning-EEG techniques, aimed at increasing validity and replicability of inter-brain synchronization studies.