Emotion Representation Mapping (ERM) has the goal to convert existing emotion ratings from one representation format into another one, e.g., mapping Valence-Arousal-Dominance annotations for words or sentences into Ekman's Basic Emotions and vice versa. ERM can thus not only be considered as an alternative to Word Emotion Induction (WEI) techniques for automatic emotion lexicon construction but may also help mitigate problems that come from the proliferation of emotion representation formats in recent years. We propose a new neural network approach to ERM that not only outperforms the previous state-of-the-art. Equally important, we present a refined evaluation methodology and gather strong evidence that our model yields results which are (almost) as reliable as human annotations, even in cross-lingual settings. Based on these results we generate new emotion ratings for 13 typologically diverse languages and claim that they have near-gold quality, at least.