Performance drop due to domain-shift is an endemic problem for NLP models in production. This problem creates an urge to continuously annotate evaluation datasets to measure the expected drop in the model performance which can be prohibitively expensive and slow. In this paper, we study the problem of predicting the performance drop of modern NLP models under domain-shift, in the absence of any target domain labels. We investigate three families of methods (H-divergence, reverse classification accuracy and confidence measures), show how they can be used to predict the performance drop and study their robustness to adversarial domain-shifts. Our results on sentiment classification and sequence labelling show that our method is able to predict performance drops with an error rate as low as 2.15% and 0.89% for sentiment analysis and POS tagging respectively.