The second-order nonlinear optical coefficients of 4H-SiC and 6H-SiC have been measured by use of two second-harmonic generation methods, the rotational Maker-fringe and wedge techniques, at the fundamental wavelength of $1.064\mu \mathrm{m}$ . Measurements on high-quality (0001) and $\left(11\overline{2}0\right)$ plane samples as well as rigorous analyses taking into account the multiple-reflection effects allowed us to accurately determine the magnitudes of the nonlinear optical coefficients. The obtained values are $d_{31}=6.7\mathrm{pm}∕\mathrm{V}$ , $d_{15}=6.5\mathrm{pm}∕\mathrm{V}$ , and $d_{33}<!--?xpp\; bf?-->=-12.5\mathrm{pm}∕\mathrm{V}$ for 6H-SiC; and $d_{31}=6.5\mathrm{pm}∕\mathrm{V}$ , $d_{15}=6.7\mathrm{pm}∕\mathrm{V}$ , and $d_{33}=-11.7\mathrm{pm}∕\mathrm{V}$ for 4H-SiC.