Characteristic mode analysis (CMA) provides useful insights for the design of dielectric resonator antennas (DRAs). In this paper, an interpolation method is proposed to reduce the computational burdens of volume equivalence principle (VEP) based CMA. The CMA is performed at several discrete frequencies, and the eigencurrents and eigenvalues at intermediate frequencies are obtained using efficient polynomial interpolation. Several examples such as rectangular, hollow, and inhomogeneous DRAs are computed and compared with verified results.