Localization - assigning sufficiently accurate positions to nodes - in Wireless Sensor Networks (WSNs) has attracted research among various strategies, some using Received Signal Strength Indication (RSSI) at nodes. Nodes with known position, called anchors, may be fixed or mobile. Position may be computed by global optimization, or locally between anchors and nodes. For Wireless Rechargeable Sensor Networks (WRSNs), a charger may act as a mobile anchor enabling high-resolution localization for efficient RF charging. This study describes a hybrid scheme for localization and charging of WRSNs using an Unmanned Aerial Vehicle (UAV) carrying a node and an RF charger. It works reliably under log-normal fading of RSSI due to shadowing. RSSI localization brings the UAV close enough to the node to elicit a response from the RF charger. Time of Charge is then used to position the UAV accurately above the node, to allow for charging with maximum efficiency.