In this paper, we propose an object-based camera pose estimation from a single RGB image and a pre-built map of objects, represented with ellipsoidal models. We show that contrary to point correspondences, the definition of a cost function characterizing the projection of a 3D object onto a 2D object detection is not straightforward. We develop an ellipse-ellipse cost based on level sets sampling, demonstrate its nice properties for handling partially visible objects and compare its performance with other common metrics. Finally, we show that the use of a predictive uncertainty on the detected ellipses allows a fair weighting of the contribution of the correspondences which improves the computed pose. The code is released at gitlab.inria.fr/tangram/level-set-based-camera-pose-estimation.