You may be able to select everything on your map and Scale it up to the size of the grid.
I cheat with things like this and use bits of tape on my monitor to know the exact size I have to scale it to. This is because you won't be able to scale the grid, that will have to be hidden.
So mark the corners of your grid. Hide it in the layers.
Scale select all items on the map, and make sure you scale and position it in the marks you've made on your screen.
This may work.
Also some of the super talented CCII & III user's may have better quicker ways to do this.