Procedures to perform reliable relativistic self-consistent-field (RSCF) calculations are described. Using light atoms and molecules, it is demonstrated that the present method always yields correct nonrelativistic limit by employing a sufficiently large value for the speed of light in RSCF calculations. Many problems associated with analytic expansions of the Dirac equations can be computationally avoided by kinetically balancing the basis sets for large and small component spinors. Results of RSCF calculations for Ne, Kr, $H_2$, and LiH indicate very small relativistic effects for these systems as expected. Trends found is these molecules, however, may be useful in understanding relativistic effects for molecules with similar valence electronic structures and heavier atoms.