Given a set of trajectories demonstrating the execution of a task safely in a constrained MDP with observable rewards but with unknown constraints and non-observable costs, we aim to find a policy that maximizes the likelihood of demonstrated trajectories trading the balance between being conservative and increasing significantly the likelihood of high-rewarding trajectories but with potentially unsafe steps. Having these objectives, we aim towards learning a policy that maximizes the probability of the most $promising$ trajectories with respect to the demonstrations. In so doing, we formulate the ``promise" of individual state-action pairs in terms of $Q$ values, which depend on task-specific rewards as well as on the assessment of states' safety, mixing expectations in terms of rewards and safety. This entails a safe Q-learning perspective of the inverse learning problem under constraints: The devised Safe $Q$ Inverse Constrained Reinforcement Learning (SafeQIL) algorithm is compared to state-of-the art inverse constraint reinforcement learning algorithms to a set of challenging benchmark tasks, showing its merits.