Heat a grill to high. Brush the tomatoes with olive oil and season with salt and pepper. Grill until slightly charred and soft, flipping halfway through, 4 to 6 minutes.
Place the tomatoes, honey, chipotle, horseradish, Worcestershire sauce, lime juice, cilantro, a pinch each of salt and pepper and a touch of olive oil in a food processor and process until slightly smooth. Serve with grilled shrimp.
To cook the shrimp, toss with vegetable oil and season with salt and pepper; grill over medium-high heat until marked and opaque, 2 to 3 minutes per side.