Segmenting terminal villous structures as separable instances is a prerequisite task for quantitative and explainable analysis of placental histopathology. Inspired by the fact that villous structure is typically surrounded by syncytiotrophoblast cells which yield critical hints for segmentation, we focus on designing a contour-based instance segmentation method. Previous contour-based methods usually utilize the confidence of object localization (or classification) as the instance score, without contour scores which explicitly measure the contour refinement quality (i.e., the distance discrepancy between the predicted contour and its ground truth). In this paper, we propose an augmented contour Scoring Snake framework, termed as SSnake, which learns both contour deformation and refinement quality estimation. To form contour quality measurement, we devise an axis-aware size-adaptive smooth function mapping from predicted contours to normalized scores in point resolution. Besides, to estimate scores of long-distance cases and strengthen the score learning process, a contour-augmented training scheme is designed for initial box contours. Our method recalibrates instance scores using contour quality by prioritizing instances with finer contours. Experimental results on the in-house separable villi segmentation dataset and a public cell nucleus segmentation dataset demonstrate that our proposed method significantly outperforms all competitors including state-of-the-art approaches. In villi segmentation dataset, our proposed SSnake achieves 3.7% improvements in COCO APm over the baseline DeepSnake. The source code is available at https://github.com/Psilym/SSnake.