Unmanned aerial vehicle (UAV)-assisted microwave wireless power transfer (WPT) enables the deployment of radio frequency (RF)-power-driven, battery-less sensor nodes in rural areas such as farm fields. Unlike in urban areas, suitable ambient radio waves for RF energy harvesting are not available in rural areas, therefore, we propose using UAVs to carry active RF sources. The UAVs will cover large fields and function as movable power feeders. To feed power to sensor nodes or any power feeding target efficiently, a UAV needs to be navigated to the desired power feeding point, which is usually right above the target; however, a Global Positioning Services (GPS) system is not accurate enough for this purpose. Therefore, this paper presents two trilateration-inspired sensor node position estimation methods for UAV WPT, based on the relationship between the sensor-UAV distance and power transmission efficiency. After the UAV collects data of several distances, measured by the sensor node from different UAV locations, the UAV then estimates the position of a sensor node by utilizing the data. In the direction-based approach, circles with the radius set as the measured distance are first centered at the measurement positions. Then, all the intersections of the two circles are calculated. Further, by relying on the assumption that the sensor node would be in the direction where the largest number of intersections is observed, the average position of the intersections included in the direction is regarded as the estimated position of the sensor. In the least squares approach, the position that minimizes the sum of squares of errors, obtained from the measurement results, is assumed to be the sensor position. By comparing the direction-based and least squares approaches to the conventional hill climbing method, we found that the least squares and direction-based approaches can complete power feeding faster in average by 52% and 26%, respectively, compared to the hill climbing method. Combining GPS with our least squares approach will enable the UAV to reach the appropriate zone rapidly and complete the power supply process quickly so that power may be delivered to more sensor nodes in less time.