Wind energy resource assessments for Pentecost Island and Epi Island in Vanuatu were carried out using one year of wind data. The wind data were used to calculate the daily average wind speed, diurnal variation of wind speed and monthly average wind speed. The diurnal variation of wind shear coefficient of the site was also studied and it correlated well with the temperature variation. Ten methods were used to determine the Weibull parameters and the wind power density of the site. The best method was determined using the goodness of fit test/error where the correlation coefficient, coefficient of efficiency, root mean square error, maximum absolute error and maximum absolute percentage error for the 10 methods were compared. It was found that the moments method was the best method for obtaining the shape parameter (k), the scale parameter (A) and the correct wind power density for the Pentecost Island site, whereas for the Epi site, the median and quartiles method performed the best. The mean wind speed for the Pentecost site was 5.60 m/s, while that for the Epi site was 5.86 m/s. The Weibull parameters were also estimated for the two seasons for both the islands. The wind resource maps showing the wind power density were also obtained. The annual energy production from 10 Vergnet 275 kW wind turbines, positioned at good locations on the digital wind map, was estimated. Finally, an economic analysis of the turbines was carried out, which indicated a payback period of 4.85 years.