Combine the pineapple juice and honey in a medium saucepan over medium-high heat. Bring to a simmer and cook until slightly thickened, about 15 minutes. Add the tequila and continue to cook for 2 more minutes. Turn off the heat and set aside.
Meanwhile, prepare a barbecue or grill pan to medium-high. Spread the butter over each peach half and grill, flat-sides down, until warmed through, about 4 minutes. Add the grilled peaches to the tequila syrup and let stand 20 minutes before serving.
Serve the peaches with frozen yogurt and drizzle with tequila syrup.
Cook's Note: The peaches can stand in the syrup, covered, up to 2 hours at room temperature.