Recent architectures integrate high-performance and power-efficient matrix engines. These engines demonstrate remarkable performance in low-precision matrix multiplication, which is crucial in deep learning. Several techniques have been proposed to emulate single- and double-precision general matrix-matrix multiplication (SGEMM and DGEMM, respectively) by leveraging such low-precision matrix engines. In this study, we present emulation methods that significantly outperforms conventional approaches. On a GH200 Grace Hopper Superchip, the proposed DGEMM emulation achieves a 1.4x speedup and a 43% improvement in power efficiency compared to native DGEMM for sufficiently large problems. The proposed SGEMM emulation achieves a 3.0x speedup and a 154% improvement in power efficiency compared to native SGEMM for sufficiently large problems. Furthermore, compared to conventional emulation methods, the proposed emulation achieves more than 2x higher performance and superior power efficiency.