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Deep learning methods have been employed in gravitational-wave astronomy to accelerate the construction of surrogate waveforms for the inspiral of spin-aligned black hole binaries, among other applications. We face the challenge of modeling the residual error of an artificial neural network that models the coefficients of the surrogate waveform expansion (especially those of the phase of the waveform) which we demonstrate has sufficient structure to be learnable by a second network. Adding this second network, we were able to reduce the maximum mismatch for waveforms in a validation set by 13.4 times. We also explored several other ideas for improving the accuracy of the surrogate model, such as the exploitation of similarities between waveforms, the augmentation of the training set, the dissection of the input space, using dedicated networks per output coefficient and output augmentation. In several cases, small improvements can be observed, but the most significant improvement still comes from the addition of a second network that models the residual error. Since the residual error for more general surrogate waveform models (when e.g., eccentricity is included) may also have a specific structure, one can expect our method to be applicable to cases where the gain in accuracy could lead to significant gains in computational time.