We propose a novel approach to approximate numerically shock waves. The method combines the unstructured shock-fitting approach developed in the last decade by some of the authors, with ideas coming from embedded boundary techniques. The numerical method obtained allows avoiding the re-meshing phase required by the unstructured fitting method, while guaranteeing accuracy properties very close to those of the fitting approach. This new method has many similarities with front tracking approaches, and paves the way to shock-tracking techniques truly independent on the data and mesh structure used by the flow solver. The approach is tested on several problems showing accuracy properties very close to those of more expensive fitting methods, with a considerable gain in flexibility and generality.