The interplay between superconductivity and structural phase transition has attracted enormous interest in recent years. For example, in Fe-pnictide high temperature superconductors, quantum fluctuations in association with structural phase transition have been proposed to lead to many novel physical properties and even the superconductivity itself. Here we report a finding that the quasi-skutterudite superconductors (Sr 1−x Ca x ) 3 Ir 4 Sn 13 (x = 0, 0.5, 1) and Ca 3 Rh 4 Sn 13 show some unusual properties similar to the Fe-pnictides, through 119 Sn nuclear magnetic resonance (NMR) measurements. In (Sr 1−x Ca x ) 3 Ir 4 Sn 13 , the NMR linewidth increases below a temperature T * that is higher than the structural phase transition temperature T s . The spin-lattice relaxation rate (1/T 1 ) divided by temperature (T ), 1/T 1 T and the Knight shift K increase with decreasing T down to T * , but start to decrease below T * , and followed by more distinct changes at T s . In contrast, none of the anomalies is observed in Ca 3 Rh 4 Sn 13 that does not undergo a structural phase transition. The precursory phenomenon above the structural phase transition resembles that occurring in Fe-pnictides. In the superconducting state of Ca 3 Ir 4 Sn 13 , 1/T 1 decays as exp(−∆ /k B T ) with a large gap ∆ = 2.21k B T c , yet without a Hebel-Slichter coherence peak, which indicates strong-coupling superconductivity. Our results provide new insight into the relationship between superconductivity and the electronic-structure change associated with structural phase transition.