In modern electrophysiology, ablation therapy for supraventricular arrhythmias is guided by local voltage and conduction velocity. State-of-the-art mapping techniques use multiple bipolar electrogram measurements to assess these quantities, both of which depend on the estimation of the electric field. This field is commonly approximated using a first-order Taylor expansion. To improve the approximation of its two-dimensional projection, we propose a second-order expansion of the electric potential by extending the least-squares estimation to include the additional parameters required to approximate the Hessian matrix. Electric-field estimates obtained using first- and second-order Taylor expansions are compared with a reference field derived from a finite-difference approximation to the negative extracellular potential gradient. The latter is generated by simulating two scenarios in a cuboid tissue slab: a planar and a curved wavefront. We investigate the effects of the number of bipolar measurements and their distances from the reference location. Compared with the reference field, the second-order Taylor method yields a greater improvement over the first-order method for the curved wave than for the planar wave. Specifically, the mean relative RMSE difference between the second- and first-order methods decreases from -4.44 % for the planar wave to -15.02 % for the curved wave.