During the past few decades, satellite altimetry has brought tremendous new knowledge about the spatial and temporal variations of sea surface heights over the Earth's oceans. However, the precision is limited over short wavelengths and in coastal areas, and other methods such as kinematic GPS may be needed to fill in this information. We present kinematic GPS work aimed at mapping the sea surface height, with special attention to the precision one can expect. Active marine subduction zones, like the Vanuatu archipelago, may present short wavelength, high amplitude undulations of the sea surface height that are difficult to map with satellite altimetry. This paper presents the methodology used around Santo Island, in Vanuatu, to obtain a well-resolved local sea surface map with a precision of 5-15 cm limited by the sea conditions and the distance from the coastal reference station. We present the results of three campaigns in 2004, 2006 and 2007. Careful observation of the ship behaviour along the surveys as well as simultaneous recording of the ship attitude variations is mandatory to obtain reliable results. We show that the ship GPS antenna height varies with the ship's velocity and we suggest a method to correct this effect. The final precision is estimated using the crossover differences method.