In bone regeneration, silicon-based calcium phosphate glasses (Bioglasses) have been widely used since the 1970s. However, they dissolve very slowly because of their high amount of Si (SiO2 > 45%). Recently, our group has found that calcium ions released by the degradation of glasses in which the job of silicon is done by just 5% of TiO2 are effective angiogenic promoters, because of their stimulation of a cell-membrane calcium sensing receptor (CaSR). Based on this, other focused tests on angiogenesis have found that Bioglasses also have the potential to be angiogenic promoters even with high contents of silicon (80%); however, their slow degradation is still a problem, as the levels of silicon cannot be decreased any lower than 45%. In this work, we propose a new generation of hybrid organically modified glasses, ormoglasses, that enable the levels of silicon to be reduced, therefore speeding up the degradation process. Using electrospinning as a faithful way to mimic the extracellular matrix (ECM), we successfully produced hybrid fibrous mats with three different contents of Si (40, 52, and 70%), and thus three different calcium ion release rates, using an ormoglass-polycaprolactone blend approach. These mats offered a good platform to evaluate different calcium release rates as osteogenic promoters in an in vivo subcutaneous environment. Complementary data were collected to complement Ca2+ release analysis, such as stiffness evaluation by AFM, zeta-potential, morphology evaluation by FESEM, proliferation and differentiation analysis, as well as in vivo subcutaneous implantations. Material and biological characterization suggested that compositions of organic/inorganic hybrid materials with a Si content equivalent to 40%, which were also those that released more calcium, were osteogenic. They also showed a greater ability to form blood vessels. These results suggest that Si-based ormoglasses can be considered an efficient tool for calcium release modulation, which could play a key role in the angiogenic promoting process.