Strong-coupling effects on the upper critical fields H-c2 along the c axis in the noncentrosymmetric heavy fermion superconductors near quantum criticality CeRhSi3 and CeIrSi3 are examined. For sufficiently large spin-orbit interactions due to the lack of inversion symmetry, H-c2 is mainly determined by the orbital depairing effects. From microscopic calculations taking into account the strong spin fluctuations, we show that H-c2 is extremely enhanced as the system approaches the quantum critical point, resulting in H-c2 similar to 30 T even in the case of a low transition temperature T-c(H=0)similar to 1 K, which explains well the huge H-c2 observed in the recent experiments.