3D Magnetic Resonance Imaging (MRI) is often a trade-off between fast but low-resolution image acquisition and highly detailed but slow image acquisition. Fast imaging is required for targets that move to avoid motion artefacts. This is in particular difficult for fetal MRI. Spatially independent upsampling techniques, which are the state-of-the-art to address this problem, are error prone and disregard contextual information. In this paper we propose a context-sensitive upsampling method based on a residual convolutional neural network model that learns organ specific appearance and adopts semantically to input data allowing for the generation of high resolution images with sharp edges and fine scale detail. By making contextual decisions about appearance and shape, present in different parts of an image, we gain a maximum of structural detail at a similar contrast as provided by high-resolution data. We experiment on 145 fetal scans and show that our approach yields an increased PSNR of 1.25 dB when applied to under-sampled fetal data cf. baseline upsampling. Furthermore, our method yields an increased PSNR of 1.73 dB when utilizing under-sampled fetal data to perform brain volume reconstruction on motion corrupted captured data.