Meditation is a self-regulatory process practiced primarily to reduce stress, manage emotions and mental health. The objective was to study the information exchange between symmetric electrodes across the hemispheres during meditation using functional connectivity (FC) measures. We investigate the changes in the coherence between EEG electrode pairs during the meditation practiced by long-term Brahmakumaris Rajyoga meditators with open eyes and during listening to music by controls as the comparable task. Two distinct FC measures derived from coherency, namely, magnitude squared coherence (MSC) and imaginary part of coherency (ICoh) are used to study the changes in interhemispheric coherence. During baseline conditions, higher MSC is found in meditators in frontocentral and centroparietal regions and higher |ICoh| globally in higher beta and gamma bands than controls. Further, in meditators, the MSC significantly increases in higher theta and alpha bands in the frontal and parietal regions and |ICoh| significantly decreases across all regions and bands except in the alpha band during meditation. However, the control subjects with no knowledge of meditation show no change in theta or alpha MSC or |ICoh| during the music session. Distinct patterns of changes are observed with the two FC measures in different frequency bands during meditation in the meditators and music-listening session in the control subjects indicating varied information processing between the right and left hemispheres and differences in the FC measures used. We found increased MSC and decreased |ICoh| between the frontal electrodes implying increased self-awareness in meditators. The MSC between the occipital electrodes in meditators is less than the controls in baseline condition indicating a possible modified visual information processing in Rajyoga meditators due to the long-term practice of meditation with open eyes. Overall, the changes in MSC indicate increased functional integration during meditation supporting the hypothesis of cortical integration theory.