To apply reinforcement learning to safety-critical applications, we ought to provide safety guarantees during both policy training and deployment. In this work we present novel theoretical results that provide a bound on the probability of violating a safety property for a new task-specific policy in a model-free, episodic setup: the bound, based on a 'maximum policy ratio' that is computed with respect to a 'safe' base policy, can also be more generally applied to temporally-extended properties (beyond safety) and to robust control problems. We thus present SPoRt, which also provides a data-driven approach for obtaining such a bound for the base policy, based on scenario theory, and which includes Projected PPO, a new projection-based approach for training the task-specific policy while maintaining a user-specified bound on property violation. Hence, SPoRt enables the user to trade off safety guarantees in exchange for task-specific performance. Accordingly, we present experimental results demonstrating this trade-off, as well as a comparison of the theoretical bound to posterior bounds based on empirical violation rates.