Two ionic liquids (ILs) based on the BF4- anion are studied by H-1, B-11, and F-19 NMR spectroscopy by measuring self-diffusion coefficients (D) and spin-lattice relaxation times (T-1). The cations are 1-ethyl-3-methylimidazolium (EMIm) and 1-butyl-3-methylimidazolium (BMIm). Since two NMR nuclei (B-11 and F-19) of BF4- exhibit narrow lines and high sensitivity, the B-11 and F-19 NMR measurements of D-BF4 and T-1(BF4) were performed in a wide temperature range. The temperature-dependent behaviors of T-1(F-19) and T-1(B-11) were remarkably different, although the values of D-BF4(F-19) and D-BF4(B-11) almost agreed. Since the Arrhenius plots of T-1's for H-1, F-19, and B-11 exhibited T-1 minima, the correlation times tau(c)(H-1), tau(c)(F-19), and tau(c)(B-11) were evaluated. The D(cation) and D(BF4) were plotted against 1/tau(c)(H-1) and 1/tau(c)(F-19), respectively, and the relationships between translational and rotational motion are discussed. The translational diffusion of the cations is related to molecular librational motion and that of BF4 is coupled with reorientational motion. The tau(c)(B-11) derived from B-11 T-1 can be attributed to a local jump. From the plots of the classical Stokes-Einstein (SE) equation, the empirical c values, which were originally derived by theoretical boundary conditions, were estimated for each ion. The empirical c(BF4) was about 4.4(5), while the c values of the cations were smaller than 4.