Preheat the oven to 400°F (200°C).
Score the skin of the duck breasts in a crosshatch pattern.
Season the duck breasts with salt and pepper.
Heat olive oil in a skillet over medium-high heat. Place duck breasts skin-side down and sear until golden brown, about 6-8 minutes.
Flip the duck breasts and sear the other side for 2-3 minutes before transferring to the oven.
Roast the duck in the preheated oven for about 10-12 minutes, or until a meat thermometer reads 135°F (57°C) for medium-rare.
Remove duck from the oven, cover with foil, and let rest for 5-10 minutes.
In the same skillet, add cherries, port wine, honey, and balsamic vinegar. Cook until the sauce thickens, about 5-7 minutes.
Taste the sauce and adjust seasoning, if needed.
Slice the duck breasts and serve drizzled with cherry-port sauce.