We report X-ray diffraction and electron spin resonance (ESR) measurements of the effect of SrTiO3 ceramics doping using Cu2+ ions. ESR measurements reveal two kinds of Cu2+ centers in weakly (0.2-0.5 mol% Cu) doped SrTiO3. Both kinds of centers have been attributed to Cu2+ at octahedral Ti sites and possibly associated either with a nearest-neighboring oxygen vacancy (center #1) or some other positively charged defect (center #2). The ESR spectra of the above centers are described by the following spin Hamiltonian parameters: g (aEuro-) = 2.263(1), g (aSyen) = 2.041(1), A (aEuro-) = 170(1) x 10(-4) cm(-1), A (aSyen) = 27(1) x 10(-4) cm(-1) (center #1) and g (aEuro-) = 2.334(1), g (aSyen) = 2.059(1), A (aEuro-) = 137(1) x 10(-4) cm(-1), A (aSyen) a parts per thousand 0(1) x 10(-4) cm(-1) (center #2). For copper concentration larger than 2 mol%, the antiferromagnetic SrCu3Ti4O12 (SCTO) phase has been detected by both X-ray diffraction and ESR. Its volume increases with increase of Cu concentration reaching about 17 % at Cu doping of 20 mol%. The composite SrTiO3-SCTO ceramics exhibits substantial magnetocapacitance effect, which could be enhanced by electrostriction of SrTiO3.