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Coastal populations are impacted by relative sea level variations, which consist both of absolute sea level variations and of vertical land motions. This paper focuses on the Southwest and Central Pacific region, a recognized vulnerable region to sea level rise and where a large range of vertical land motion dynamics is observed. We analyse vertical displacement rates obtained from Global Navigation Satellite Systems (GNSS) by different analysis centres. We study the role played by modelled parameters, such as step discontinuities (due to equipment changes, earthquakes, etc.), in the position time-series analysis. We propose a new modelling approach based on a joint inversion of GNSS position time-series from different analysis centres. The final uncertainty on the vertical land motion rates is estimated as a combination of the uncertainty due to the GNSS data processing itself and the uncertainty due to the stability of the reference frame in which the GNSS data are expressed. We find that the dominant trend in the Southwest and Central Pacific is a moderate subsidence, with an average rate of -1.1 mm yr(-1), but significant variations are observed, with displacement rates varying from an uplift of 1.6 +/- 0.3 mm yr(-1) to a subsidence of -5.4 +/- 0.3 mm yr(-1). Taking into account the geodynamic context, we assess, for each station, the relevance of current estimates of linear vertical displacement rate and uncertainty for forecasting future coastal sea levels.