Pose estimation is essential for many applications within computer vision and robotics. Despite its uses, few works provide rigorous uncertainty quantification for poses under dense or learned models. We derive a closed-form lower bound on the covariance of camera pose estimates by treating a differentiable renderer as a measurement function. Linearizing image formation with respect to a small pose perturbation on the manifold yields a render-aware Cramér-Rao bound. Our approach reduces to classical bundle-adjustment uncertainty, ensuring continuity with vision theory. It also naturally extends to multi-agent settings by fusing Fisher information across cameras. Our statistical formulation has downstream applications for tasks such as cooperative perception and novel view synthesis without requiring explicit keypoint correspondences.