This study introduces an entropy-guided boundary supervision method to address boundary leakage and false-positive activations in breast ultrasound segmentation. The proposed loss function scales contour penalties by per-pixel predictive entropy and ground-truth maps, focusing gradient emphasis on uncertain lesion margins. Evaluated on the BUSI dataset, the method preserved lesion segmentation quality with a mean Dice score of 0.7624, statistically indistinguishable from the baseline. However, it significantly improved specificity by reducing false-positive activations on no-lesion images from 19 of 20 to 5 of 20. A post-hoc spatial temperature scaling step further reduced the expected calibration error from 0.0201 to 0.0095 without altering segmentation masks. These results demonstrate that entropy-guided supervision and spatial calibration function as complementary refinements within a U-Net framework.