Time series classification is a task which deals with temporal sequences, a prevalent data type common in domains such as human activity recognition, sports analytics and general sensing. In this area, interest in explainability has been growing as explanation is key to understand the data and the model better. Recently, a great variety of techniques have been proposed and adapted for time series to provide explanation in the form of saliency maps, where the importance of each data point in the time series is quantified with a numerical value. However, the saliency maps can and often disagree, so it is unclear which one to use. This paper provides a novel framework to quantitatively evaluate and rank explanation methods for time series classification. We show how to robustly evaluate the informativeness of a given explanation method (i.e., relevance for the classification task), and how to compare explanations side-by-side. The goal is to recommend the best explainer for a given time series classification dataset. We propose AMEE, a Model-Agnostic Explanation Evaluation framework, for recommending saliency-based explanations for time series classification. In this approach, data perturbation is added to the input time series guided by each explanation. Our results show that perturbing discriminative parts of the time series leads to significant changes in classification accuracy, which can be used to evaluate each explanation. To be robust to different types of perturbations and different types of classifiers, we aggregate the accuracy loss across perturbations and classifiers. This novel approach allows us to recommend the best explainer among a set of different explainers, including random and oracle explainers. We provide a quantitative and qualitative analysis for synthetic datasets, a variety of timeseries datasets, as well as a real-world case study with known expert ground truth.