Silicon Photomultipliers (SiPMs) have recently been recognized as an interesting alternative to photomultiplier tubes (PMTs) thanks to their high sensitivity and time resolution. They can closely approach quantum-limited sensitivity in the detection of weak optical signals. Ifremer (French Research Institute for Exploitation of the Sea) and Institut Fresnel research lab have been investigating appropriate alternative solutions for PMTs in the context of underwater optical communications, and have for the first time used these new photodetector components for signal detection. A novel prototype of an optical modem based on SiPM receivers was realized with support from Osean SAS Co., a French instrumentation company. A number of lab experiments and sea trials in turbid waters and clear open sea were conducted using this modem to evaluate the practical interest of SiPMs. This paper studies the feasibility of using SiPMs for underwater optical communications. It outlines the description of the transmitter and the receiver of the modem prototype, the different techniques used to take advantage of this new technology and solutions to possible practical challenges. It also presents the methodology of the conducted sea trials and the performance evaluations in terms of range and data rate.