Private insurance is the other legal route in Italy, but pricing is set by each insurer individually — there is no official government price to quote, so get quotes directly from two or three providers rather than trusting a number from a blog.
The travel insurance you need before you even land
This is the one most students forget entirely. Both Germany and Italy, as Schengen states, require proof of travel medical insurance with at least €30,000 in coverage before they will issue your visa in the first place. This is separate from, and comes before, the statutory or SSN insurance you arrange once you are actually enrolled and resident. Missing or under-covered travel insurance is one of the documented reasons Schengen student visas get refused, so buy a policy that explicitly states the €30,000 minimum on the certificate, not just a general travel plan.

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