This paper proposes Characteristic Examples for effectively fingerprinting deep neural networks, featuring high-robustness to the base model against model pruning as well as low-transferability to unassociated models. This is the first work taking both robustness and transferability into consideration for generating realistic fingerprints, whereas current methods lack practical assumptions and may incur large false positive rates. To achieve better trade-off between robustness and transferability, we propose three kinds of characteristic examples: vanilla C-examples, RC-examples, and LTRC-example, to derive fingerprints from the original base model. To fairly characterize the trade-off between robustness and transferability, we propose Uniqueness Score, a comprehensive metric that measures the difference between robustness and transferability, which also serves as an indicator to the false alarm problem. Extensive experiments demonstrate that the proposed characteristic examples can achieve superior performance when compared with existing fingerprinting methods. In particular, for VGG ImageNet models, using LTRC-examples gives 4X higher uniqueness score than the baseline method and does not incur any false positives.