The EPR spectra of high-T-c superconducting composites with the formula YBa2Cu3-xScxO6.5 +/- delta (x = 0-1.1) over the temperature range 300-77 K are reported. The study reveals that unusually large-scale substitution of SC3+ for Cu2+ results in high-T-c superconducting materials with paramagnetic phases which are well resolved above T-c. Paramagnetism is suppressed below T-c with the dominance of the diamagnetic -superconducting phase which is EPR-silent. However, the composite with the nominal formula YBa2Cu2ScO7 +/- delta is the exception. For this sample, the EPR spectrum remains well resolved also below T-c, exhibiting only a local symmetry change of a paramagnetic center when decreasing the temperature below T-c. The study presented in this paper has revealed that the paramagnetic signal over, corresponds to the impurity phases and the EPR signal recorded below T-c, for x = 0.8-1.1, is due to the dominance of the spinellike Ba(CuSc)O-3.5 phase.