In jyotisha blue sapphire is neelam, the gem of Shani, Saturn, and it occupies a distinctive place in the navaratna: it is held to be the fastest-acting of the nine gems and the most dangerous.
The tradition around it is unusually specific and is worth reporting accurately, because it is the clearest example of a gem prescription that comes with its own contraindication. Practitioners hold that neelam produces its effect immediately, within days or even hours, and that the effect is unambiguously good or unambiguously bad according to whether Saturn is well placed for the wearer. The customary procedure is a trial period, the stone worn briefly and removed if misfortune follows. It is not to be worn casually, and reputable practitioners will refuse to prescribe it without a chart.
That structure, a powerful remedy with a built-in test, is common to serious divinatory and remedial traditions and is worth distinguishing from the generic beneficence of most modern crystal literature, where no stone ever does harm and none is ever unsuitable. Whatever one thinks of the underlying claim, the jyotisha material is making a falsifiable-shaped assertion and the popular Western material generally is not.
The Western tradition assigns sapphire quite differently, most often to Jupiter or to the Sun by way of its heavenly and royal associations, and Agrippa pairs sapphire with the fixed star Capella in the Behenian scheme. These are not variants of one tradition; they are separate systems that happen to use the same stone, and reconciling them is not possible and should not be attempted.
Sapphire is the September birthstone on the 1912 list.