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How do you go about getting insurance for large tanks in case they leak?

Some brands have a warranty. Maybe you can add it to your renters/home owners insurance. As long as the glass is not cracked, you can reseal it yourself. It's not hard but a bit time consuming.

No, I mean to insure the building in case it causes damage to my apartment? Add it to the renters insurance?

Yes, I would check with the renters insurance policy. Tanks also don't normally spontaneously leak, usually the point of source is a filter.

Check with your insurance but you should be covered, weather it's fish tank, bath tub, dishwasher, waterbed etc. They should replace everything damaged including that tank, but not the livestock.