General progressive Type-II censoring is widely applied in life-testing experiments to enhance efficiency by allowing early removal of surviving units, thereby reducing experimental time and cost. This paper develops exact inference and prediction procedures for one- and two-parameter exponential models based on multiple independent general progressively Type-II censored samples. Using the recursive algorithm repeatedly, exact confidence intervals for model parameters and exact prediction intervals for unobserved failure times are constructed. The proposed methods are illustrated with simulated and real (tire wear) data, demonstrating their practical applicability to partially censored reliability experiments.