Maritime transport faces increasing pressure to reduce its greenhouse gas emissions to be in accordance with the Paris Agreement. For this to happen, low- and zero-carbon energy solutions need to be developed. In this paper we draw on sustainability transition literature and introduce the technological innovation system (TIS) framework to the field of maritime transportation research. The TIS approach analytically distinguishes between different innovation system functions that are important for new technologies to develop and diffuse beyond an early phase of experimentation. This provides a basis for technology-specific policy recommendations. We apply the TIS framework to the case of battery-electric and hydrogen energy solutions for coastal maritime transport in Norway. Whereas both battery-electric and hydrogen solutions have developed rapidly, the former is more mature and has a strong momentum. Public procurement and other policy instruments have been crucial for developments to date and will be important for these technologies to become viable options for shipping more generally.