For the how part referred to in the previous answer, conforming Quad or Hex mesh refinement is most likely going to use an algorithm based on the work of R. Schneiders' 2- and 3- refinement algorithms. These methods are used in mesh generation. Two papers that I happen to have that do adaptive conforming quad refinement are:
"A new fast hybrid adaptive grid generation technique for arbitrary two-dimensional domains" by Ebeida et al, Int. J. Num. Meth. Eng. 84:305-329 (2010) who use 2-refinement algorithms and show time dependent examples,
and a preprint
"Conformal Refinement of Unstructured Quadrilateral Meshes" by Garimella, who uses 3-refinement and whose source I don't remember. (Both of these are 2-D, but Schneiders presents 3D algorithms, too.)
The question refers to applying a conforming algorithm using some local error estimate. The papers I cite show adaptive, local (h-)refinement, but don't say much about the decision of when to subdivide and coalesce. For the spectral approximation, one approach would be to use an element-local interpolation estimate like Cathy Mavriplis did in her dissertation, or an adjoint based estimate like that used by Matt Willyard in his dissertation. These would indicate that an element needs to be refined. You could then apply the conforming h-adaptation as in the papers above to satisfy the prediction that the estimate provides.
The spectral algorithm, however, will prefer to increase the order over subdividing elements if the solution is smooth. That will lead to (functionally) non-conforming meshes locally. If that is the question that is really being asked, then no, I don't see a way of doing conforming order refinement.