Zero-dimensional (0D) cardiovascular models are reduced order models, based on dynamical systems, aimed to model the whole-body blood circulation. They are based on electric-hydraulic analogy leading to a system of differential-algebraic equations. Despite the tremendous speed gain than three-dimensional models in predictions, tasks such as sensitivity analysis, parameter estimation, or uncertainty quantification are still expensive to perform since they need tens of thousands of simulations. To speed up these tasks, surrogate models are built offline for the 0D models and can be used to perform these tasks faster than 0D models. We assess different strategies to build the models namely neural networks (NN), polynomial chaos expansion, and Gaussian processes. It was found from numerical experiments that neural networks have the best performance overall in terms of accuracy and computational efficiency when tested on 3 different 0D models. NN was later used to perform the whole pipeline for performing sensitivity analysis, parameter estimation, and uncertainty quantification. The process was quite fast mainly due to the automatic differentiation capability that exists in deep learning libraries as TensorFlow allowing to perform gradient-based optimization leading to fast parameter estimation. In general, it should be noted that NN is favored when the whole pipeline is needed due to the simplicity of usage and implementation. However, the other surrogate modeling methods are favored in specific tasks, for example, obtaining the Sobol indices using PCE is usually automatic with no extra computational cost, while GP is favored for obtaining confidence intervals for the predictions.