Preheat the oven to 425 degrees F. Line a cookie sheet with foil, then place a wire rack on top.
For the chicken tenders: Mix the cracker crumbs and Parmesan together in a large bowl. In a shallow dish, mix the mayonnaise, mustard, cider vinegar and some salt and pepper.
Sprinkle the chicken tenders with a little salt and pepper and then place them, one by one, in the mayonnaise mixture. Scrape off excess mayonnaise and then roll the tenders in the crumb mixture to coat. As you go, place the coated tenders on the wire rack.
Bake until cooked through and golden brown, 25 minutes. Let cool on the rack for 5 minutes.
For the Dijon sauce: Meanwhile, in a small bowl, combine the mustard, mayonnaise, honey, cayenne and some salt and pepper. Mix until smooth and lump free.
Transfer the chicken tenders to a serving platter. Serve with the Dijon sauce.