Quantitative conductivity mapping (QCM) techniques use the first spatial derivatives and/or the Laplacian of the B1 phase. These are commonly estimated by fitting a 3D quadratic function within a kernel around each voxel. However, small kernels lead to severe noise amplification and large kernels induce inaccuracies. Here we determined the optimal kernel radii across a range of magnitude SNR using an anthropomorphic, numerical brain phantom. The optimal kernel size decreased with increasing SNR. Calculating the first derivatives required smaller kernels than calculating the Laplacian making QCM methods using first derivatives likely more accurate than Laplacian-based techniques.