The contribution of this paper is two-fold. First, we show how to extend the ESM algorithm to handle motion blur in 3D object tracking. ESM is a powerful algorithm for template matching-based tracking, but it can fail under motion blur. We introduce an image formation model that explicitly consider the possibility of blur, and shows its results in a generalization of the original ESM algorithm. This allows to converge faster, more accurately and more robustly even under large amount of blur. Our second contribution is an efficient method for rendering the virtual objects under the estimated motion blur. It renders two images of the object under 3D perspective, and warps them to create many intermediate images. By fusing these images we obtain a final image for the virtual objects blurred consistently with the captured image. Because warping is much faster than 3D rendering, we can create realistically blurred images at a very low computational cost.