Volumetric measurements of fetal structures in MRI are time consuming and error prone and therefore require automatic segmentation. Placenta segmentation and accurate fetal brain segmentation for gyrification assessment are particularly challenging because of the placenta fuzzy boundaries and the fetal brain cortex complex foldings. In this paper, we study the use of the Contour Dice loss for both problems and compare it to other boundary losses and to the combined Dice and Cross-Entropy loss. The loss is computed efficiently for each slice via erosion, dilation and XOR operators. We describe a new formulation of the loss akin to the Contour Dice metric. The combination of the Dice loss and the Contour Dice yielded the best performance for placenta segmentation. For fetal brain segmentation, the best performing loss was the combined Dice with Cross-Entropy loss followed by the Dice with Contour Dice loss, which performed better than other boundary losses.