An old three pence piece is worth face value at around 3 pennies. It is an obsolete coin in the United Kingdom and is even more obsolete in the United States.
According to the Coins of the United Kingdom, a small publication by coin expert Tony Clayton, the three pence ceased to be legal tender in 1971. Since they are not legal tender in either the United States or the United Kingdom it is difficult to even obtain face value for them.
A three pence coin that has not been circulated at all, is in mint condition and carries a certificate will bring around $10 in the United States. Most collectors will not even pay that price unless they are in desperate need of the piece to complete a specific collection. These types of three pence coins are not worth a lot because there were so many of them made. There is nothing spectacular about them that could make them rare or cause them to be valuable to collectors.
Due to the fact that so few were made during the year, a 1946 three pence is more valuable than any of the other three pence dates. It is a somewhat common coin and will bring double the amount of a three pence coin from another date. For around $20, a collector who is in need of the 1946 year can get this three pence coin.