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We describe in detail our implementation of a modulation phase shift (MPS) technique for narrow-bandwidth measurement of differential group delay (DGD) and the principal states of polarization (PSP) in optical fibers and components. Our MPS technique involves launching six orthogonal polarization states (as opposed to the four states typically launched) to achieve improved measurement stability. The measurement bandwidth is 4.92 GHz (twice the 2.46 GHz RF modulation frequency), the measurement time is 13 s per point, and the single-measurement uncertainty is better than 40 fs (∼95% confidence interval) for DGD values from 10 to 1000 fs. We demonstrate that this uncertainty can be greatly improved by averaging, yielding a 9.7 fs uncertainty (95% confidence interval) on a device with 315 fs of DGD. Sources of uncertainty are detailed, including a DGD contribution from the detector itself. Simulations illustrate the uncertainty contribution of multiple DGD elements in series.