Deep reinforcement learning (DRL) has become a dominant deep-learning paradigm for various tasks in which complex policies are learned within reactive systems. In parallel, there has recently been significant research on verifying deep neural networks. However, to date, there has been little work demonstrating the use of modern verification tools on real, DRL-controlled systems. In this case-study paper, we attempt to begin bridging this gap, and focus on the important task of mapless robotic navigation -- a classic robotics problem, in which a robot, usually controlled by a DRL agent, needs to efficiently and safely navigate through an unknown arena towards a desired target. We demonstrate how modern verification engines can be used for effective model selection, i.e., the process of selecting the best available policy for the robot in question from a pool of candidate policies. Specifically, we use verification to detect and rule out policies that may demonstrate suboptimal behavior, such as collisions and infinite loops. We also apply verification to identify models with overly conservative behavior, thus allowing users to choose superior policies that are better at finding an optimal, shorter path to a target. To validate our work, we conducted extensive experiments on an actual robot, and confirmed that the suboptimal policies detected by our method were indeed flawed. We also compared our verification-driven approach to state-of-the-art gradient attacks, and our results demonstrate that gradient-based methods are inadequate in this setting. Our work is the first to demonstrate the use of DNN verification backends for recognizing suboptimal DRL policies in real-world robots, and for filtering out unwanted policies. We believe that the methods presented in this work can be applied to a large range of application domains that incorporate deep-learning-based agents.