Term translation quality in machine translation (MT), which is usually measured by domain experts, is a time-consuming and expensive task. In fact, this is unimaginable in an industrial setting where customised MT systems often need to be updated for many reasons (e.g., availability of new training data, leading MT techniques). To the best of our knowledge, as of yet, there is no publicly-available solution to evaluate terminology translation in MT automatically. Hence, there is a genuine need to have a faster and less-expensive solution to this problem, which could help end-users to identify term translation problems in MT instantly. This study presents a faster and less expensive strategy for evaluating terminology translation in MT. High correlations of our evaluation results with human judgements demonstrate the effectiveness of the proposed solution. The paper also introduces a classification framework, TermCat, that can automatically classify term translation-related errors and expose specific problems in relation to terminology translation in MT. We carried out our experiments with a low resource language pair, English-Hindi, and found that our classifier, whose accuracy varies across the translation directions, error classes, the morphological nature of the languages, and MT models, generally performs competently in the terminology translation classification task.