Visual-language foundation models, like CLIP, learn generalized representations that enable zero-shot open-set classification. Few-shot adaptation methods, based on prompt tuning, have been shown to further improve performance on downstream datasets. However, these methods do not fare well in the taxonomic open set (TOS) setting, where the classifier is asked to make prediction from label set across different levels of semantic granularity. Frequently, they infer incorrect labels at coarser taxonomic class levels, even when the inference at the leaf level (original class labels) is correct. To address this problem, we propose a prompt tuning technique that calibrates the hierarchical consistency of model predictions. A set of metrics of hierarchical consistency, the Hierarchical Consistent Accuracy (HCA) and the Mean Treecut Accuracy (MTA), are first proposed to evaluate TOS model performance. A new taxonomic open set (ProTeCt) technique is then proposed to calibrate classification across label set granularities. Results show that ProTeCt can be combined with existing prompt tuning methods to significantly improve TOS classification without degrading the leaf level classification performance.