We have applied the Tremaine-Weinberg continuity equation method to derive the bar pattern speed in the SB(r) b galaxy NGC 2523 and the SB(r) 0/a galaxy NGC 4245 using the calcium triplet absorption lines. These galaxies were selected because they have strong inner rings which can be used as independent tracers of the pattern speed. The pattern speed of NGC 2523 is 26.4 +/- 6.1 kms(-1) kpc(-1), assuming an inclination of 49.7 degrees and a distance of 51.0 Mpc. The pattern speed of NGC 4245 is 75.5 +/- 31.3 km s(-1) kpc(-1), assuming an inclination of 35.4 degrees and a distance of 12.6 Mpc. The ratio of the corotation radius to the bar radius of NGC 2523 and NGC 4245 is 1.4 +/- 0.3 and 1.1 +/- 0.5, respectively. These values place the bright inner rings near and slightly inside the corotation radius, as predicted by barred galaxy theory. Within the uncertainties, both galaxies are found to have fast bars that likely indicate dark halos of low central concentration. The photometric properties, bar strengths, and disk stabilities of both galaxies are also discussed.