Drain the cherry juice into a large saucepan and set the cherries aside.
Add the port, beef broth, horseradish, tomato paste, shallot, bay leaf, and peppercorns.
Bring to a boil over medium heat and cook until the mixture is reduced to about 2/3 cup, 12 to 15 minutes.
Dissolve the arrowroot in 1 teaspoon water and stir into the sauce.
Simmer until the sauce is shiny and slightly thickened, 1 minute longer.
Strain, cover, and set aside (This can be prepared a few hours ahead if you refrigerate the sauce, bring it to room temperature before proceeding.)
Heat the olive oil in a large, heavy skillet over high heat.
Sprinkle the steaks with salt and pepper and add them to the hot oil.
Brown the steaks on both sides and cook until medium-rare (about 6 minutes total) or to your liking.
Transfer the steaks to a large platter.
Add the cherries and kirsch to the skillet and flambé. When the flames die out, reduce the heat to low and add the cherry sauce. With a wooden spoon, scrape up any browned bits from the bottom of the pan.
Stir in the butter and grenadine syrup, the sauce should be bright red.
Cook until the beef is heated through, about 2 minutes longer.
Season the sauce to taste with salt and pepper, if necessary.
Transfer the beef tenderloin steaks to warmed dinner plates.
Spoon the cherry sauce over them and serve at once.