Rinse the wild rice under cold water. Combine it with the chicken broth and 1 tablespoon of butter in a medium saucepan. Bring to a boil, then reduce to low heat, cover, and simmer for 45 minutes until the rice is tender and the liquid is absorbed.

While the rice cooks, score the skin of each duck breast in a crosshatch pattern. Season both sides with the salt and pepper.

Heat a smoker to 225°F. Place the duck breasts skin side up on the grates and smoke for about 1 hour until the internal temperature reaches 135°F for medium-rare.

In a skillet, heat the olive oil and remaining tablespoon of butter over medium heat. Add the shallot and cook until softened. Stir in the cherries, port wine, and thyme sprigs. Simmer for 8 to 10 minutes until the sauce thickens slightly.

Remove the duck from the smoker and let it rest for 5 minutes. Slice the breasts against the grain and serve over the wild rice with the cherry port sauce spooned on top.