I've done a little reading on sand and permanent casting but a rapier seems like it may be thin for that kind of manufacture.
What methods and tools would have been used to make it?
(Please provide sources for your answer so that we might perform expanded research.)
Since times immemorial, most all types of swords were made by forging rather than casting.
Casting a sword is visually appealing, which is why you see that in the movies, but was not used in practice for multiple reasons, foremost of which were metallurgical concerns.
Casting steel requires significantly higher temperatures than forging (~1400°C vs. ~800°C) and unless you have a modern mould (along with a bunch of other modern metalurgical trappings), is likely to introduce impurities and faults into the material. This would be an expensive error, because getting an ingot of good steel would have been a non-trivial endeavour during most of history.
In contrast, forging is much gentler on the ingot, only takes two days or thereabouts (for the blade, that is) and hammering the blade can improve its properties with certain types of materials.
Also, the finished blade would usually quenched and tempered to keep it from bending.
First of all, swords are made from steel and casting steel is an advanced technology not available in the 17th century.
Swords and all other steel tools are forged, which means that the steel ingot is hammered into shape.
The rapier was original to Toledo and at one time that city exported swords to all parts of Europe. Later, of course, their work was widely imitated and you can find rapiers made all over. Besides Toledo, Solingen in Germany became known as a good producer.
The distinguishing characteristic of the rapier is its strength and flexibility which was tested by bending the sword around the waist. This is only possible if the steel is very good quality and has manganese and is well tempered. Original rapiers were broader than what we call a rapier today, being more similar to what we now call an epee.
The technique for making a true Toledo is a complex art which varied from swordmaker to swordmaker. The general strategy was to first hammer the ingot into a long strip which was then divided into three pieces. The pieces would then be forged together, the central one forming a core. Sword specialists call this type of construction a "welded" blade. By varying temperature of the core and the cladding it is possible to give the two parts a different temper which is essential to the suppleness of the sword. Finally the sword would be given a final tempering to harden the edge.
Die casting is a technique which has been in vogue since the last 250 to 300 years. Forging is a classic technique which has extensively been used since the ancient period both in Asia and Europe. Die casting requires a machine to press dies out of casting sand then a foundry to raise the metal to such a high temperature that it liquefies and at last pour the metal. It may create a sword but till now the swords are considered at the same time a weapon and an art piece with all the grains in it that the master swordsmiths incorporate in the metal after a lot of cutting folding twisting and turning. these grains will not be available if swords are made in dies. again the process of cuts and folds and strikes makes the steel uniform throughout in carbon content and adds extra plasticity to the material which will never be achieved in the cast piece even after a series of quenching and tempering. moreover forging allows us mix more than one quality of steel together retaining their basic properties. whereas cast iron is allover homogeneous. the Japanese katana or the samurai swords are an example of the above process of forging where hard high carbon steel is combined with low carbon soft steel to produce a one of its kind blade which is at the same time so strong as to knock a tree down and so sharp as to slice a human being from head to groin in a single blow. the strength of the blade is due to the hard steel and the razor edge is the consequence of the soft steel which had made the katana one of the deadliest weapons in the pre firearms age. so forging is a technique which allows steel to be used not only as a metal for making implements but also it allows the smith add a touch of artistic and asthetic value to the implement which the foundry can never do. moreover the forged materials go through a cycle of quenching and annealing which causes them to become flexible and strong at the same time which is a quality the rapier is supposed to have. Even in modern times we use forges for different implement making than diecasting them.
