Nonlinear optical borate crystals of ${\mathrm{Gd}}_{1-x}{\mathrm{Sc}}_x{\mathrm{Ca}}_4\mathrm{O}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_3$ and ${\mathrm{Gd}}_{1-x}{\mathrm{Lu}}_x{\mathrm{Ca}}_4\mathrm{O}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_3$ have been grown and characterized. By changing the composition of these crystals, their optical birefringence can be controlled to obtain second-harmonic generations (SHG) in the ranges of $790–824\mathrm{nm}$ along the Y axis and $920–963\mathrm{nm}$ along the Z axis through noncritical phase matching (NCPM). The refractive indices of grown crystals were measured with a minimum-deviation technique. The experimental results of NCPM conditions for SHG are in good agreement with the theoretical predictions.