Preheat the oven to 350 degrees F and grease or spray a 13x9 inch baking dish and set aside.
Make sure to set the cold ingredients out, so they can come closer to room temperature before making the batter. This will keep the batter from clumping up and will help it mix better.
In a medium-sized bowl, combine the flour, baking soda, baking powder and salt. Whisk well and set aside.
In another bowl, add the cherry yogurt, chopped cherries, ⅓ cup reserved maraschino cherry juice and vanilla extract. Whisk well and set aside.
In a large mixing bowl, add the room-temperature butter and the sugar and mix with an electric mixer on medium-high speed for two minutes until light and fluffy.
Add the eggs one at a time and mix on medium speed for just 20 seconds after adding each egg.
Scrape down the sides and bottom of the bowl and mix again on medium, only until everything is well incorporated.
Alternately add in the dry mixture and the liquid mixture to the butter mixture, starting and ending with the dry mixture.
(Add in ⅓ of the dry mixture and mix on medium just until combined. Add in ½ the liquid mixture, mixing on medium only until combined. Add in another ⅓ of the dry mixture, mixing on medium only until combined. Add in the last of the liquid mixture, mixing on medium only until combined, then the last of the dry mixture and mixing on medium until combined.)
Be very careful only to mix until just combined. Mixing too long and at too high of a speed can cause the cake to come out dense, rubbery or to fall in the middle.
Scrape down the sides of the bowl and mix again only for 7-10 seconds or so.
Pour the batter into the prepared pan and bake at 350 degrees F on the middle rack for approximately 30-35 minutes. Ovens vary.
The cake is fully baked when a toothpick inserted into the center comes out with a few moist crumbs on it or clean, but no raw batter.
Remove the cake from the oven and place onto a wire rack to cool completely while you make the buttercream.