Preheat the oven to 375 degrees F. Combine the coriander, cumin, peppercorns and garlic in a mortar and pestle (or use a heavy skillet, placing spices on cutting board); coarsely crush the spices, and season with salt. Rub the pork tenderloin with the spice mixture.
Heat the oil in a large oven-proof skillet over medium heat until very hot; add the tenderloin. Cook the pork, turning occasionally, until browned on all sides, about 6 minutes total. Add the limes or lemon, cut-side down, to the skillet. Transfer the skillet to the oven.
Roast the pork until just cooked through, or until an instant-read thermometer inserted into the thickest part of the pork registers 150 degrees F, about 15 minutes. Let stand 5 minutes; slice, squeeze the citrus juice over the pork, and serve with pan juices and a favorite side dish.
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