Paving the path toward the fifth generation (5G) of wireless networks with a huge increase in the number of user equipment has strengthened public concerns on human exposure to radio-frequency electromagnetic fields (RF EMFs). This requires an assessment and monitoring of RF EMF exposure, in an almost continuous way. Particular interest goes to the uplink (UL) exposure, assessed through the transmission power of the mobile phone, due to its close proximity to the human body. However, the UL transmit (TX) power is not provided by the off-the-shelf modem and RF devices. In this context, we first conduct measurement campaigns in a multi-floor indoor environment using a drive test solution to record both downlink (DL) and UL connection parameters for Long Term Evolution (LTE) networks. Several usage services (including WhatsApp voice calls, WhatsApp video calls, and file uploading) are investigated in the measurement campaigns. Then, we propose an artificial neural network (ANN) model to estimate the UL TX power, by exploiting easily available parameters such as the DL connection indicators and the information related to an indoor environment. With those easy-accessed input features, the proposed ANN model is able to obtain an accurate estimation of UL TX power with a mean absolute error (MAE) of 1.487 dB.