Fencing in the SCA began with modern foil and epee but quickly progressed to using the schlager as a commercially available, more accurate reproduction of a period rapier. Unfortunately, due to it's construction, a schlager is a poor reproduction of a period rapier. This is because a schlager blade does not taper either in profile (width) or distally (thickness). A rapier blade does both, tapering in all directions towards the tip creating a lighter, longer blade with more of the weight towards the wielders hand allowing finer control of the tip.
Various commerical artisans in the SCA recognized this and set out to procure reproduction rapiers from established sword makers. Del Tin Armi Antiche in Italy was one of the first sword foundries that began supplying reproduction rapiers with rebated edges. They have since been followed by the Paul Chen / Hanwei / CAS Iberia practical rapiers, the Triplette supplied Zamorano and T03 rapiers, Darkwood Armoury's own branded Darkwood rapiers, Alchem Inc.'s Safeflex rapier and the Angus Trim practice rapier.
Refer to the SCA Society Rapier Marshal's Blade Types and Conventions to determine what reproduction rapier blades a specfic kingdom has authorized.