Certain coins become valuable over time due to their rarity, which, in turn, is a result of their age, some error, or just overall condition. The coins with a minting or design mistake, called mules or error coins, can fetch high prices when resold by private collectors or put up for sale at an auction. This is why many consider such coins great investments. Today, a few valuable European coins might be worth considering. 

1. 2008 Portugal 1 Euro First Map Mule
This error coin features the outdated map of Europe, which was found on Euro coins from 2002 to 2007.

2. Greek 2 Euro Coin with a Finnish Detail
Also among the 10 best coins to buy, these 2 Euro coins have a unique feature that boosts their value to over 1,000 euros (or £852) on marketplaces.

3. 20 Euro Cent with Two Reverse Dies
A rare set of Eurozone coins, issued between 1999 and 2007, were accidentally struck with two reverse sides and no obverse by a die—a metallic piece used to strike a coin. This set is among coins with high returns, as the error makes them valued collectables. For instance, one such coin sold for nearly £1,002 at an auction. That said, if looking for a coin from this set, one should be careful, as altered, near-identical versions of the coin may be passed off as authentic. Malicious sellers may join the two halves of the coins and make a mutilated, altered coin. One can look for seams around the coin edge or examine the weight to avoid falling for scams while investing in valuable coins.

4. 1 Euro Cent With Two Reverse Dies
Like the 20 Euro cent, there is a 1 Euro cent coin with two reverse sides without an obverse. This is also a valuable coin , as recently , it sold for £296.  

5. 2008 Great Britain 20 Pence Mule
This British coin features the wrong obverse. Instead of a dated Queen side, it has an undated obverse. The issue occurred because an old obverse design was used with the new royal shield of arms reverse in 2008. The Royal Mint estimates that fewer than 250,000 of the 136 million 20-pence coins were minted without the year, and they are still in circulation, with some valued at £77.

6. 2009 Great Britain 10 Pence Mule
Another example of a coin with high returns is the Great Britain 10 Pence Mule of 2009. It has just two or three known coins currently in circulation. The coin has the wrong, older reverse design that was supposed to be discontinued in 2008. The design had a single crowned lion in the centre with the denomination below. So, there’s a rare probability that anyone will encounter an error version of the coin with the old reverse design. As it is rarer than other such mules, the 10 Pence coin is known to sell for £771–£1,156.

7. French Euro 2001 Mint Error
What makes this coin highly sought-after is a minting error, wherein the wrong planchet was used. This coin was struck on a 20-cent blank instead of a 1 Euro one. The coin might be worth considering, as it was previously sold for £709.

8. French 50 Euro Cent on a 2-Cent Planchet
As the name suggests , here , a 50 Euro Cent coin was stamped on the planchet (a round metal disk meant to be struck as a coin) for a 2 Euro Cent coin. Consequently, it turned into a copper-coloured coin that stands out. Previously, the coin fetched a price of £166.

9. Vatican Euro Coin with Two Reverses
This extremely rare Vatican Euro error coin features two reverses, i.e., it has no heads. On one side, the coin has a 20-cent design , and on the other, it has a 50-cent design. While the exact number of these coins is not yet known, one of them sold for £2,217.

10. 2007 Monaco Grace Kelly 2 Euro Coin
In 2007, Monaco released a special 2 Euro coin featuring the profile of its former princess and actress Grace Kelly. This limited edition coin marked the 25th anniversary of her tragic death. A total of 20,001 coins were minted—20,000 meant for public distribution and one as a gift for Prince Albert II (Kelly’s son). This coin had the smallest circulation of any commemorative 2 Euro coin between 2007 and 2014. Each coin was initially sold for €120 (or £102). Although the price seemed to be high even then, collectors today can sell it for nearly £3,407. 

If considering investing in coins or starting a collection, it is important to do some research, find reliable sellers and auction sites, and then look up pictures of coins worth a lot of money to begin the search.