For determining precise sea surface heights, six marine GNSS (global navigation satellite system) survey campaigns were performed in the eastern Baltic Sea in 2021. Four GNSS antennas were installed on the vessel, the coordinates of which were computed relative to GNSS–CORS (continuously operating reference stations). The GNSS–CORS results are compared to the PPP (precise point positioning)-based results. Better accuracy is associated with the GNSS–CORS postprocessed points; however, the PPP approach provided more accurate results for longer than 40 km baselines. For instance, the a priori vertical accuracy of the PPP solution is, on average, 0.050 ± 0.006 m and more stable along the entire vessel’s survey route. Conversely, the accuracy of CORS-based solutions decreases significantly when the distances from the GNSS–CORS exceed 40 km, whereas the standard deviation between the CORS and PPP-based solutions is up to 0.075 m in these sections. Note that in the harbor (about 4 km from the nearest GNSS–CORS), the standard deviation of vertical differences between the two solutions remains between 0.013 and 0.024 m. In addition, the GNSS antennas situated in different positions on the vessel indicated different measurement accuracies. It is suggested for further studies that at least one GNSS antenna should be mounted above the mass center of the vessel to reduce the effects of the dominating pitch motion during the surveys.