Weinhold’s formula for the upper and lower bounds to transition moments is extended to include transitions between states of the same symmetry. Chong’s semirigorous expression for the lower bound to the overlap between the approximate and the true wavefunctions is studied and applied to the calculation of error limits for the dipole moments and transition moments of LiH at R=3.015 bohr. With high-quality wavefunctions, the results are: μ (X 1Σ+) =5.836±0.262 D; μ (A 1Σ+) =−5.078±0.344 D; w (X 1Σ+) =0.94 (+0.13, −0.18); w (X 1Σ+−B 1Π) =1.29±0.23 ea0; and w (A 1Σ+−B 1Π) =1.82±0.24 ea0.