The Sig Sauer is the informal name of a gun (inferred to be a pistol) which is the preferred weapon of Domovoi Butler.Foaly commented in the The Arctic Incident regarding the gun's bullets, saying 'one of these could blow your head off'.
In general, SIG Sauer Inc. manufactures several high-end handguns, any of which could be a suitable choice for a well equipped professional bodyguard. Given Foaly's comments regarding the destructive power of the gun's cartridges, it is likely that these are .45ACP which could mean any one of several models including the SIG P220 or SIG GSR. Indeed it is likely that Butler owns several different models of handgun manufactured by SIG Sauer Inc.
Interestingly, on the Australian cover of Artemis Fowl and in the graphic novels, Butler's rifle resembles a machine gun rather than a pistol. This could be taken to mean that among the weapons in Butler's arsenal is a SIG MG 710-3.