How to remove baked on food on ceramic cooktops?

If you have some really crusty stuff. You can make a 'dam' using some hobby store modeling clay...just make a 'snake rope' and press that down. From there you can soak the area overnight with whatever you like. Baking Soda/vinegar stuff, or Hydrogen Peroxide and warm the area.

i sprinkle a liberal amount of baking soda on the cooktop and scrub down with a wet towel. i then wipe away any remaining baking soda with a separate clean, wet towel (you'll clearly see any residue you missed once the stovetop dries off a little). have never needed to use anything more. good luck!

You can use a brass scraper, which is softer than ceramic and won't scratch it. Here is one that was designed to scrape snow from auto windshields:
https://www.amazon.com/CJ-Industries-F101-Fantastic-Scraper/dp/B000FW4LT4/ref=sr_1_4?ie=UTF8&qid=1469975008&sr=8-4&keywords=Brass+snow+scraper

My 'go to' kitchen counter cleaner, which works on everything, is vinegar, water and a drop of dish soap in a bottle. Spray it on and let it sit for at least a half hour for stuck on stuff. You can also sprinkle baking soda on the 'wet' spot for hard to remove debris.

Wrights (same people who make silver polish) make a cleanser for cooktops that works well. Even Albertsons carries it.

I would definitely not try Comet--I think it could scratch the surface. I use a soft scrub cleanser formulated specifically for ceramic cook tops. The brand is Sidol, but I don’t know if this is sold in the US--but there is surely something similar. I rarely have to use it--after I’m finished cooking, I give the stove a quick wipe with a bit of detergent and dry with a paper towel. If something seems baked on, I sometimes turn the heat up full blast and whatever is there seems to bake itself off.

I'd start with a razor blade followed by a green pad with bleach-based cleaner (like Comet).

Good luck.