In a small bowl, mix to combine the lime juice, mustard, and soy sauce. Pat the tenderloin dry with paper towels and apply this mixture to the exterior of the pork. Season the meat with the coriander and salt.
Sear the pork over the hot side of the grill until the exterior forms a nice crust, about 4 minutes per side. Move the pork to the medium side of the grill, cover the grill, and cook until the pork reaches an internal temperature of 140 degrees F.