Square cooktop / round hole
 

... well, not exactly. But the old cooktop was slightly larger than my new cooktop. If I center the new one exactly I can see about a 1/16" crack on both sides. If I push it all the way to one side I have almost 1" crack to work with. The countertop is tile. Any suggestions on how to fill the space so it doesn't look like a shoddy patch-up job? Thanks!

Could you trim out the hole with ceramic tile trim of a contrasting color to fill in the hole a bit? You may need to create a bit of structure with plywood and or cement board.