Saliency methods are widely used to interpret neural network predictions, but different variants of saliency methods often disagree even on the interpretations of the same prediction made by the same model. In these cases, how do we identify when are these interpretations trustworthy enough to be used in analyses? To address this question, we conduct a comprehensive and quantitative evaluation of saliency methods on a fundamental category of NLP models: neural language models. We evaluate the quality of prediction interpretations from two perspectives that each represents a desirable property of these interpretations: plausibility and faithfulness. Our evaluation is conducted on four different datasets constructed from the existing human annotation of syntactic and semantic agreements, on both sentence-level and document-level. Through our evaluation, we identified various ways saliency methods could yield interpretations of low quality. We recommend that future work deploying such methods to neural language models should carefully validate their interpretations before drawing insights.