This work examines the charging power allocation and beam selection problem for distributed estimation in wireless passive sensor networks, where the sensors are charged over the air by RF-enabled energy sources. A two-phase replenishment and transmission cycle is considered. In the replenishment phase, each wireless charger emits power over the air through a carefully selected beam and power to replenish the wireless sensors. In the transmission phase, each sensor makes a local observation of the underlying parameter and transmits a quantized version of its measurement to the fusion center, where the final estimation is computed. The charging power allocation and beam selection are jointly determined by minimizing the mean-square error (MSE) of the final estimate. For tractability, the optimization is performed by considering an MSE upper bound as the objective function and is solved efficiently using alternating optimization and successive convex relaxation techniques. The simulation results demonstrate the effectiveness of the proposed scheme.