Prediction of wireless channel gain (CG) across space is a necessary tool for many important wireless network design problems. In this paper, we develop prediction methods that use environment-specific features, namely building maps and CG measurements, to achieve high prediction accuracy. We assume that measurements are collected using a swarm of coordinated unmanned aerial vehicles (UAVs). We develop novel active prediction approaches which consist of both methods for UAV path planning for optimal measurement collection and methods for prediction of CG across space based on the collected measurements. We propose two active prediction approaches based on deep learning (DL) and Kriging interpolation. The first approach does not rely on the location of the transmitter and utilizes 3D maps to compensate for the lack of it. We utilize DL to incorporate 3D maps into prediction and reinforcement learning for optimal path planning for the UAVs based on DL prediction. The second active prediction approach is based on Kriging interpolation, which requires known transmitter location and cannot utilize 3D maps. We train and evaluate the two proposed approaches in a ray-tracing-based channel simulator. Using simulations, we demonstrate the importance of active prediction compared to prediction based on randomly collected measurements of channel gain. Furthermore, we show that using DL and 3D maps, we can achieve high prediction accuracy even without knowing the transmitter location. We also demonstrate the importance of coordinated path planning for active prediction when using multiple UAVs compared to UAVs collecting measurements independently in a greedy manner.