Heat the oven to 350°F, or 325°F if using a dark or nonstick pan. Set the rack in the middle position so the cake bakes evenly without over-darkening at the edges.

Put the butter in a 13x9-inch pan and place the pan in the warming oven for 5 to 7 minutes. Check it near the end of that time; the butter should be fully melted but should not brown.

Remove the pan, scatter the brown sugar evenly over the butter, then arrange the pineapple rings and cherries on top. Press the fruit gently into the sugar so it stays in place as the butter and sugar begin to bubble around the edges.

Add water to the reserved pineapple juice until the total reaches 1 cup, then prepare the cake batter as directed on the box using that mixture instead of water. The batter should look smooth and pourable, with a light pineapple aroma.

Pour the prepared batter evenly over the arranged fruit. Cover the fruit completely and level the surface gently so the cake rises evenly across the pan.

Bake for 40 to 46 minutes, or 44 to 53 minutes for a dark or nonstick pan, then loosen the cake edges immediately with a knife. A toothpick inserted into the center should come out without wet batter, and the center should spring back lightly when touched.

Set a heatproof serving plate upside down over the pan and carefully turn both over together, leaving the pan in place for 5 minutes. The warm glaze will drizzle down over the cake as it releases, and a gentle tap may produce a hollow release sound.

Lift away the pan and let the cake cool for 30 minutes before serving warm or cool. The topping will settle into a glossy layer while the crumb becomes easier to slice cleanly.