The goal of this article is to address the problem of inconsistent models and the challenge it poses for perspectivism. I analyze the argument, draw attention to some hidden premises behind it, and deflate them. Then I introduce the notion of perspectival models as a distinctive class of modeling practices whose primary function is exploratory. I illustrate perspectival modeling with two examples taken from contemporary high-energy physics at the Large Hadron Collider at the European Organization for Nuclear Research (CERN), which are designed to show how a plurality of seemingly incompatible models (suitably understood) is methodologically crucial to advance the realist quest in cutting-edge areas of scientific inquiry.