Conventional frequentist federated learning (FL) schemes are known to yield overconfident decisions. Bayesian FL addresses this issue by allowing agents to process and exchange uncertainty information encoded in distributions over the model parameters. However, this comes at the cost of a larger per-iteration communication overhead. This letter investigates whether Bayesian FL can still provide advantages in terms of calibration when constraining communication bandwidth. We present compressed particle-based Bayesian FL protocols for FL and federated “unlearning” that apply quantization and sparsification across multiple particles. The experimental results confirm that the benefits of Bayesian FL are robust to bandwidth constraints.