  We extend the construction of generalized Berezin and Berezin-Toeplitz
quantization to the case of compact Hodge supermanifolds. Our approach is based
on certain super-analogues of Rawnsley's coherent states. As applications, we
discuss the quantization of affine and projective superspaces. Furthermore, we
propose a definition of supersymmetric sigma-models on quantized Hodge
supermanifolds. The corresponding quantum field theories are finite and thus
yield supersymmetry-preserving regularizations for QFTs defined on flat
superspace.
