Significance: Resting-state functional connectivity (RSFC) analyses of functional near-infrared spectroscopy (fNIRS) data reveal cortical connections and networks across the brain. Motion artifacts and systemic physiology in evoked fNIRS signals present unique analytical challenges, and methods that control for systemic physiological noise have been explored. Whether these same methods require modification when applied to resting-state fNIRS (RS-fNIRS) data remains unclear. Aim: We systematically examined the sensitivity and specificity of several RSFC analysis pipelines to identify the best methods for correcting global systemic physiological signals in RS-fNIRS data. Approach: Using numerically simulated RS-fNIRS data, we compared the rates of true and false positives for several connectivity analysis pipelines. Their performance was scored using receiver operating characteristic analysis. Pipelines included partial correlation and multivariate Granger causality, with and without short-separation measurements, and a modified multivariate causality model that included a non-traditional zeroth-lag cross term. We also examined the effects of pre-whitening and robust statistical estimators on performance. Results: Consistent with previous work on bivariate correlation models, our results demonstrate that robust statistics and pre-whitening are effective methods to correct for motion artifacts and autocorrelation in the fNIRS time series. Moreover, we found that pre-filtering using principal components extracted from short-separation fNIRS channels as part of a partial correlation model was most effective in reducing spurious correlations due to shared systemic physiology when the two signals of interest fluctuated synchronously. However, when there was a temporal lag between the signals, a multivariate Granger causality test incorporating the short-separation channels was better. Since it is unknown if such a lag exists in experimental data, we propose a modified version of Granger causality that includes the non-traditional zeroth-lag term as a compromising solution. Conclusions: A combination of pre-whitening, robust statistical methods, and partial correlation in the processing pipeline to reduce autocorrelation, motion artifacts, and global physiology are suggested for obtaining statistically valid connectivity metrics with RS-fNIRS. Further studies should validate the effectiveness of these methods using human data.