Refrigerator end panels or ability to screw to soffit or ceiling are two ways.

Refrigerator end panels are a good way and also hide the sides of the refrig.

Before:

After (in progress):
just after cabinet installation (you can see the space behind the pantry)

with fridge but without fridge panel

with fridge panel

24" deep pantry and cab over the fridge are pulled forward 6 inches to create enough depth for the fridge. Installer left the fridge panel unsecured so we could take it out for the floor installer because we didn't want quarter round. Fridge panel will be screwed in next week and the cab over the fridge does sag slightly on the right without the additional support of the the panel or the wall mounted cab on that side. To do it the installer laid a board across the stop that is screwed into the top of the pantry on one side and the wall mounted cab on the other to support the fridge cab in between as the cabs don't go to the ceiling. I hope this makes sense.

Thanks. Would having one wall on the end to attach to be enough, in addition to it being against the wall at the back? The cabinet would be 30" wide by 18" high. It would be in the corner, a wall on the right side, and a 24" wide by 36" tall wall cabinet on the left.

I went to the house to see if there's room for a refrigerator panel between the fridge and base cabinet, but there's not. The fridge is as close to the wall as it will go and there's not room to move the base cabinet that's next to the fridge on the other side of it. The fridge is right against that cabinet. The cabinets aren't going to the ceiling. I may have to get a shallower wall cabinet to go over the fridge. I was hoping to have the deeper storage.

From what I understand, if you want the 24" deep cabinet, you need the panel to support it. I was told the deepest you could go without it was 15". (My fridge is also next to a wall on the left side, and I have a panel on the right side.)

Since there's not room for the refrigerator panel between the fridge and the base cabinet, what about using something like the fridge panel, but instead of it going to the floor, shorten it and have it rest on the counterop of the base cab next to the fridge? The base cabinet is a Kraftmaid 24" wide 3-drawer cabinet, with either 1/2" or 3/4" plywood (I think it was 3/4"), backerboard, and porcelain tile, with no backsplash.