Make sure you have a sharp blade in the razor.
We bought a glass top stove which had a razor scraper with it and instructions on how to remove burnt on items, but I used this method with our ceramic stove before we got the glass top one.
Oven cleaner / Grease cleaners work well. Just spray some on top and let it sit for 10 - 20 minutes. Then wipe and it should come off nicely.
Just read the manual and make sure the cleaner is not damaging to ceramic. I don't it will be, but make sure.
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