Transition frequencies of cold molecules must be accurately evaluated to test the variance in the proton-to-electron mass ratio. Measuring the $X{}^2\Sigma (v,N)=(0,0)\to (1,0)$ transition frequency of optically trapped ${}^{174}$Yb${}^6$Li molecules is a promising method for achieving this goal. The Stark shifts induced by trap and probe (for the Raman transition) lasers are eliminated by choosing appropriate frequencies (magic frequencies) during the construction of the optical lattice. In the far-off resonance region, the Stark shift is found to be less than 10${}^{-16}$ even when the laser frequencies are detuned from the magic frequencies by $\sim$1 MHz. DOI: http://dx.doi.org/10.1103/PhysRevA.84.022507 ©2011 American Physical Society