Role-playing agents (RPAs) powered by large language models (LLMs) have been widely utilized in dialogue systems for their capability to deliver personalized interactions. Current evaluations of RPAs mainly focus on personality fidelity, tone imitation, and knowledge consistency, while overlooking emotional fidelity, a key factor that affects user experience. To this end, we propose a benchmark called EmoCharacter to assess emotional fidelity of RPAs in dialogues. EmoCharacter includes two benchmark datasets (single-turn and multi-turn dialogues), three evaluation settings, and six metrics to measure the emotional fidelity between RPAs and the characters they portray. Based on EmoCharacter, we conduct extensive evaluations on RPAs powered by seven widely used LLMs with representative role-playing methods. Our empirical findings reveal that: (1) Contrary to intuition, current role-playing methods often reduce the emotional fidelity of LLMs in dialogues; (2) Enhancing the general capabilities of LLMs does not necessarily improve the emotional fidelity of RPAs; (3) Fine-tuning or In-Context Learning based on real dialogue data can enhance emotional fidelity.