I suspect a lot of tourists end up with 3% of all their Euros in the
form of coins that they bring home, give away or leave behind.
I used to have that problem since it was simpler to just give someone a numbered note, which was easy to identify, rather than figuring out the coins I had. Cradle the coins in your hand, between you fingers and your palm. Small coins (1, 2, & 5 euro cent) are easy to identify because they are copper colored and small. The 1 and 5 cent piece are smooth and noticeably different in size . The 2 cent piece has a circumferential groove around the outside.
The 10, 20, and 50 cent pieces are brass. The 10 and 50 cent pieces have a lot of similar size small notches around the perimeter and very different in size. The 20 cent piece is in between in size and has only a few notches (7, I think).
Lastly, the largest coins, the 1 and 2 euro coins, are larger, but noticeably different in size. If that isn't enough, the 1 euro coin has intermittent milling, the 2 euro coin has uninterrupted milling around the circumference.
The only real challenge, and I've heard Germans complain about this very thing, is that the 50 cent and 1 euro coins are similar in size and easy to confuse, but the large number of small notches on the 50 is telltale.
Since I figured that out, I usually only bring home a small number of coins.