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The increasingly stringent regulations on privacy protection have sparked interest in federated learning. As a distributed machine learning framework, it bridges isolated data islands by training a global model over devices while keeping data localized. Specific to recommendation systems, many federated recommendation algorithms have been proposed to realize the privacy-preserving collaborative recommendation. However, several constraints remain largely unexplored. One big concern is how to ensure fairness between participants of federated learning, that is, to maintain the uniformity of recommendation performance across devices. On the other hand, due to data heterogeneity and limited networks, additional challenges occur in the convergence speed. To address these problems, in this paper, we first propose a personalized federated recommendation system training algorithm to improve the recommendation performance fairness. Then we adopt a clustering-based aggregation method to accelerate the training process. Combining the two components, we proposed Cali3F, a calibrated fast and fair federated recommendation framework. Cali3F not only addresses the convergence problem by a within-cluster parameter sharing approach but also significantly boosts fairness by calibrating local models with the global model. We demonstrate the performance of Cali3F across standard benchmark datasets and explore the efficacy in comparison to traditional aggregation approaches.