Boundaries of agricultural fields are important features necessary for defining the location, shape, and spatial extent of agricultural units. They are commonly used to summarize production statistics at the field level. In this study, we investigate the delineation of agricultural field boundaries (AFB) from Sentinel-2 satellite images acquired over the Flevoland province, the Netherlands, using a deep learning technique based on fully convolutional networks (FCNs). We designed a multiple dilation fully convolutional network (MD-FCN) for AFB detection from Sentinel-2 images at 10 m resolution. Furthermore, we developed a novel super-resolution semantic contour detection network (named SRC-Net) using a transposed convolutional layer in the FCN architecture to enhance the spatial resolution of the AFB output from 10 m to 5 m resolution. The SRC-Net also improves the AFB maps at 5 m resolution by exploiting the spatial-contextual information in the label space. The results of the proposed SRC-Net outperform alternative upsampling techniques and are only slightly inferior to the results of the MD-FCN for AFB detection from RapidEye images acquired at 5 m resolution.