Emojis have become an integral part of digital communication, enriching text by conveying emotions, tone, and intent. Existing emoji recommendation methods are primarily evaluated based on their ability to match the exact emoji a user chooses in the original text. However, they ignore the essence of users' behavior on social media in that each text can correspond to multiple reasonable emojis. To better assess a model's ability to align with such real-world emoji usage, we propose a new semantics preserving evaluation framework for emoji recommendation, which measures a model's ability to recommend emojis that maintain the semantic consistency with the user's text. To evaluate how well a model preserves semantics, we assess whether the predicted affective state, demographic profile, and attitudinal stance of the user remain unchanged. If these attributes are preserved, we consider the recommended emojis to have maintained the original semantics. The advanced abilities of Large Language Models (LLMs) in understanding and generating nuanced, contextually relevant output make them well-suited for handling the complexities of semantics preserving emoji recommendation. To this end, we construct a comprehensive benchmark to systematically assess the performance of six proprietary and open-source LLMs using different prompting techniques on our task. Our experiments demonstrate that GPT-4o outperforms other LLMs, achieving a semantics preservation score of 79.23%. Additionally, we conduct case studies to analyze model biases in downstream classification tasks and evaluate the diversity of the recommended emojis.