You can send coins to a professional authenticator and grader, like PCGS or NGC, who would certify the coin and place it in a serialized holder. Such "slabbed" coins are often easier to sell and command higher prices. This is a huge deal for some types, where a single point increase of grade (on a 70-point scale) turns $500 into $5000, and some where there are so many fakes that the standard best practice is to buy certified only.
Originally, they'd just have a lookup system on their site so you could see "Certificate 123456 was assigned to a 1825 half dollar, graded XF-45". If someone's selling certificate 12456, but on a 1912 nickel, red flags.
They still ended up with a problem of fake holders/certificates. Just scrape their database and get a cert number for the type and grade you're trying to sell, and pair it with a fake or lesser coin. So the next step was to include a high res photo of the coin in their repository. You could pull up a certificate and see "well, that's a 1825 half dollar in the container, but the one they graded has obviously different wear pattern, toning, die variety". This makes faking it much harder.
Notice it didn't require a blockchain though. There's a clear chain of trust back to the grading service, who has been in business for decades and established their brand and usually guarantees that if they misauthenticate a coin, they'll make the buyer whole.