We study downlink (DL) channel estimation in a multi-cell Massive multiple-input multiple-output (MIMO) system operating in a time-division duplex. The users must know their effective channel gains to decode their received DL data signals. A common approach is to use the mean value as the estimate, motivated by channel hardening, but this is associated with a substantial performance loss in non-isotropic scattering environments. We propose two novel estimation methods. The first method is model-aided and utilizes asymptotic arguments to identify a connection between the effective channel gain and the average received power during a coherence block. The second one is a deep-learning-based approach that uses a neural network to identify a mapping between the available information and the effective channel gain. We compare the proposed methods against other benchmarks in terms of normalized mean-squared error and spectral efficiency (SE). The proposed methods provide substantial improvements, with the learning-based solution being the best of the considered estimators.