High-precision cellular-based localization is one of the key technologies for next-generation communication systems. In this paper, we investigate the potential of applying machine learning (ML) to a massive multiple-input multiple-output (MIMO) system to enhance localization accuracy. We analyze a new ML-based localization pipeline that has two parallel fully connected neural networks (FCNN). The first FCNN takes the instantaneous spatial covariance matrix to capture angular information, while the second FCNN takes the channel impulse responses to capture delay information. We fuse the estimated coordinates of these two FCNNs for further accuracy improvement. To test the localization algorithm, we performed an indoor measurement campaign with a massive MIMO testbed at 3.7GHz. In the measured scenario, the proposed pipeline can achieve centimeter-level accuracy by combining delay and angular information.