In a small bowl, combine 1/4 cup honey and the mustard. In another small bowl, combine the mayonnaise and half of the blue cheese; mash with a fork until nearly smooth, then fold in the remaining blue cheese.
Season the chicken with salt and pepper, then coat each piece with the flour, shaking off any excess. In a medium nonstick skillet, melt the butter in the olive oil over medium heat. Add the chicken and cook for 5 minutes on each side. Drizzle the chicken with the remaining 1 tablespoon honey, lower the heat to medium-low and cook, shaking the pan frequently to prevent the honey from burning, for 5 minutes. Transfer the chicken to 2 plates and serve with the dips and celery sticks.