Context. Phase-referencing is a standard calibration technique in radio interferometry, particularly suited for the detection of weak sources close to the sensitivity limits of the interferometers. However, effects from a changing atmosphere and inaccuracies in the correlator model may affect the phase-referenced images, and lead to wrong estimates of source flux densities and positions. A systematic observational study of signal decoherence in phase-referencing and its effects in the image plane has not been performed yet. Aims. We systematically studied how the signal coherence in Very-Long-Baseline-Interferometry (VLBI) observations is affected by a phase-reference calibration at different frequencies and for different calibrator-to-target separations. The results obtained should be of interest for a correct interpretation of many phase-referenced observations with VLBI. Methods. We observed a set of 13 strong sources (the S5 polar cap sample) at 8.4 and 15 GHz in phase-reference mode with 32 different calibrator/target combinations spanning angular separations between 1.5 and 20.5 degrees. We obtained phase-referenced images and studied how the dynamic range and peak flux-density depend on observing frequency and source separation. Results. We obtained dynamic ranges and peak flux densities of the phase-referenced images as a function of frequency and separation from the calibrator. We compared our results with models and phenomenological equations previously reported. Conclusions. The dynamic range of the phase-referenced images is strongly limited by the atmosphere at all frequencies and for all source separations. The limiting dynamic range is inversely proportional to the sine of the calibrator-to-target separation. Not surpriseingly, we also find that the peak flux densities decrease with source separation, relative to those obtained from the self- calibrated images.