Sentinel-2 data represent a rich source of information for the community due to the free access and to the temporal-spatial coverage assured. However, some of the spectral bands are sensed at reduced resolution due to a compromise between technological limitations and Copernicus program's objectives. For this reason in this work we present a new super-resolution method based on Convolutional Neural Networks (CNNs) to rise the resolution of the short wave infra-red (SWIR) band from 20 to 10 meters, that is the highest resolution provided. This is accomplished by fusing the target band with the finer-resolution ones. The proposed solution compares favourably against several alternative methods according to different quality indexes. In addition we have also tested the use of the super-resolved band from an applicative perspective by detecting water basins through the Modified Normalized Difference Water Index (MNDWI).