Locally resonant metamaterials have the property of functioning in subwavelength regimes, which enables them to interact with elastic/acoustic waves larger than their unit cell size. These structures can be engineered to have specific band gaps where local resonance occurs, and waves with frequencies in the band gap region are attenuated. However, existing simulation techniques for transient analysis of locally resonant metamaterials face difficulties, including accuracy, especially in the band gap region, and huge computational cost. Accurate and efficient transient simulations are crucial for the industrial design of vibration isolation components, where band gap performance must be quantified early in the development process. Computational homogenization is a technique well suited for the subwavelength regime, since it replaces computationally expensive complex microstructure with an homogenized medium. Although classical FE2 computational homogenization, in which both the macroscopic problem and the unit cell problem are solved using finite elements, it remains computationally too expensive for practical use, especially when sufficient accuracy is required in the bandgap regions \cite{Paper}. We propose a modification of the computational homogenization scheme by employing Isogeometric Analysis (IGA) at the macroscale to analyze wave propagation in the metamaterial media. Since isogeometric analysis methods provide high accuracy for wave propagation \cite{Paper2}, this allows reducing the amount of the unit cell simulations thus reducing the total computational cost. We analyze the computational homogenization scheme with IGA in Galerkin and IGA collocation formulations at the macroscale, and demonstrate their performance in transient analysis of locally resonant metamaterials. By improving both accuracy and computational efficiency, the proposed approach helps bridge the gap between metamaterial concepts and practical engineering implementation.