hrm. If the pieces are hollow, you can drill some holes and inject them with epoxy. That would go a long way to upping the strength.
If it isn't hollow, as far as reinforcing the outside, most tricks you can do are either not going to add very much strength, or they're going to be so thick that they will ruin the detail.
If seriously concerned about strength, you might have better luck just using that piece as a guide and building a copy out of wood.