The primary means for electronic position fixing in use in contemporary maritime transport are shipborne GPS (Global Positioning System) receivers or DGPS (Differential GPS) receivers. More advanced GNSS (Global Navigation Satellite System) or RNSS (Regional Navigation Satellite Systems) receivers are able to process combined signals from American GPS, Russian GLONASS, Chinese Beidou (BDS), European Galileo, Indian IRNSS, and Japan QZSS. Satellite-based augmentation systems (SBAS) are still not commonly used in the maritime domain, especially onboard vessels certified under international SOLAS convention. The issues and weaknesses of existing International Maritime Organization recommendations, guidelines, requirements, performance standards, and policies on GNSS shipborne sensors are discussed and presented in the paper. Many problems that have already been dealt with in other means of transportation are still to be solved in the maritime domain. The integrity monitoring is addressed as the main issue, and recommendations based on solutions implemented in aviation and the latest research are proposed. Finally, the strengths, weaknesses, opportunities, and threats awaiting maritime GNSS standardization process are outlined.