Commoditization and broad adoption of machine learning (ML) technologies expose users of these technologies to new security risks. Many models today are based on neural networks. Training and deploying these models for real-world applications involves complex hardware and software pipelines applied to training data from many sources. Models trained on untrusted data are vulnerable to poisoning attacks that introduce "backdoor" functionality. Compromising a fraction of the training data requires few resources from the attacker, but defending against these attacks is a challenge. Although there have been dozens of defenses proposed in the research literature, most of them are expensive to integrate or incompatible with the existing training pipelines. In this paper, we take a pragmatic, developer-centric view and show how practitioners can answer two actionable questions: (1) how robust is my model to backdoor poisoning attacks?, and (2) how can I make it more robust without changing the training pipeline? We focus on the size of the compromised subset of the training data as a universal metric. We propose an easy-to-learn primitive sub-task to estimate this metric, thus providing a baseline on backdoor poisoning. Next, we show how to leverage hyperparameter search - a tool that ML developers already extensively use - to balance the model's accuracy and robustness to poisoning, without changes to the training pipeline. We demonstrate how to use our metric to estimate the robustness of models to backdoor attacks. We then design, implement, and evaluate a multi-stage hyperparameter search method we call Mithridates that strengthens robustness by 3-5x with only a slight impact on the model's accuracy. We show that the hyperparameters found by our method increase robustness against multiple types of backdoor attacks and extend our method to AutoML and federated learning.