We give examples of spectral triples, in the sense of A. Connes, constructed using the algebra of Toeplitz operators on smoothly bounded strictly pseudoconvex domains in C, or the star product for the Berezin–Toeplitz quantization. Our main tool is the theory of generalized Toeplitz operators on the boundary of such domains, due to Boutet de Monvel and Guillemin. VERSION – 2.1, February 11, 2014 1Research supported by GA CR grant no. 201/12/G028. 2Mathematics Institute, Silesian University in Opava, Na Rybnicku 1, 74601 Opava, Czech Republic, and Mathematics Institute, Academy of Sciences, Žitna 25, 11567 Prague 1, Czech Republic 3Aix-Marseille Universite, CNRS, CPT, UMR 7332, 13288 Marseille France, et Universite de Toulon