Background: Source-reconstructed magneto- and electroencephalography (M/EEG) are promising tools for investigating the human functional connectome. To reduce data, decrease noise, and obtain results directly comparable to magnetic resonance imaging (MRI), M/EEG source data can be collapsed into a cortical parcellation. For most collapsing approaches, however, it remains unclear if collapsed parcel time series accurately represent the coherent source dynamics within each parcel. New method: We introduce a collapse-weighting-operator optimization approach that maximizes parcel fidelity, i.e., the phase correlation between original source dynamics and collapsed parcel time series, and thereby the accuracy with which the source dynamics are retained in forward and inverse modeling. Results: The sparse, optimized weighting operator increased parcel fidelity 57-73% and true positive rate of interaction mapping from 0.33 to 0.84 in comparison to a non-sparse weighting approach. These improvements were robust for variable source topographies and parcellation resolutions. Critically, in real inverse-modeled MEG data, the optimized operator yielded close-to-perfect intra-parcel coherence. Comparison with existing methods: Previous suggestions for obtaining parcel time series include averaging all source time series within each anatomical parcel or using exclusively the time series of the voxel with maximum power. These methods are sensitive to signal heterogeneity and outlier sources. The approach advanced here avoids these problems. Conclusions: The optimized operator is suitable for collapsing real source-reconstructed M/EEG data into any cortical parcellation. The enhanced time series reconstruction fidelity yields improved accuracy of subsequent analyses of both local dynamics and large-scale interaction mapping.