How did the ancients make blanks that were (more or less) uniform in weight? Personally I think they made the molten metal into a strip or thin bar, then cut pieces of equal size/weight and then remelted each piece into a round blob. After cooling the blob was pounded flat and then struck with the dies.
I believe they would make the blanks first, then individually weigh them on a scale to make sure they were within tolerance. If too large, they would shave off pieces until it was good. if it was too small, they would toss it back in the melting pot.
More likely... based on the finding of many small crucibles... and the work of Ron Landis at Gallery Mint Museum... they were made by weighing out grain, nuggets, or clippings into cups, melting those pre-weighed masses into blobs or "buttons" as they're called, and then struck hot before they completely cooled, using bronze dies.
That makes more sense! I was thinking about some non-ancient precious metal coins that had mint-produced "shaving" marks where some small pieces were removed.
There's no one single answer to this question as there were many different methods and one could write 1,000 pages on the subject and still not have the full picture. During the Roman Republic for instance, silver coins seem to have been measured "Al marco" - essentially X pounds of bullion = Y coins. Individual coin weights were less important than batch weights. They attempted to make all coins be a similar weight by making similar sized impressions in the molds the blanks were cast in but severely overweight and underweight coins do exist. They also had a process for adjusting the size of a batch that was overweight where they gouged individual coins to remove some silver and lessen the weight of the batch and there's a paper out there on the process by Clive Stannard if you are interested in learning more.
Here's an interesting example of one of the ways of making bronze coin flans. This coin bears evidence of the process: In this case, the flan mold was actually two pieces, each one of which had round impressions made in it with channels linking them. The sides weren't perfectly aligned so you can see a ridge on the side of the coin that shows the channel and shows how far misaligned the sides were.
See this site for an interesting analysis - be sure to click through all the pages for a good overview. Weight was less important when it came to bronze coins, as they were token currency anyway.
On Sunday, @davidh posted several video links about coin production, including this one about Melle (Nouvelle-Aquitaine, France) where the old - ancient and medieval - silver mines are now a museum. They also mint "the old fashioned way" there, to find out how it was done in former times. A little bit like the medieval Guédelon castle currently being built, except this is about coins. Here is some info in English about coins from Melle: http://home.eckerd.edu/~oberhot/melle.htm (The link to the Mines and Minting Museum is outdated, see here http://www.mines-argent.com/ instead.) Christian
In some cases, perhaps they did, but ancient coins often show traces of where the sprue from the casting process has been cut off, such as this silver denarius of Julia Domna, which shows a piece of the sprue remaining at the 9:00 position: Note also this bronze pentassarion of Gordian III and Tranquillina, minted at Anchialus in Thrace. At the 6:00 position on the obverse, you can see a chunk missing from the flan where the sprue was broken off:
