The mass of a supermassive black hole (MBH) is a fundamental property that can be obtained through observational methods. Constraining MBH through multiple methods for an individual galaxy is important for verifying the accuracy of different techniques, and for investigating the assumptions inherent in each method. However, there exist only a few galaxies where multiple MBH determination techniques can be applied. NGC 4151 is one of these rare galaxies for which multiple methods can be used, stellar and gas dynamical modeling because of its proximity and reverberation mapping because of its active accretion. In this work, we reduced the integral field unit spectroscopy of the nucleus of NGC 4151 from Onken et al., observed in the H band with Gemini North NIFS, improving the process itself as well as the analysis of the spatially-resolved spectra. We also improved on the methods for constraining the line of sight velocity distribution as a function of position within the nucleus. Stellar dynamical modeling was then performed over a range of choices of MBH and mass-to-light ratio, as well as the de-projected luminosity density for various inclinations. The best reproduction of the observed kinematics and luminosity density was found with MBH = 2.44 +/- 0.16 x 10^7 MSun and mass-to-light ratio = 0.318 +/- 0.003 MSun/LSun and an inclination of 45 degrees. This measurement falls within the range of values in the literature; it is below the reverberation mapping mass of Bentz et al. (3.59 +0.45 -0.37 x 10^7 MSun) and above the reverberation mapping mass of De Rosa et al. (1.97 +/- 0.04 x 10^7 MSun), and within the uncertainties on both the gas dynamical modeling mass of Hicks & Malkan (3.0 +0.8 -2.2 x 10^7 MSun) and the stellar dynamical modeling mass of Onken et al. (3.60 +/- 1.10 x 10^7 MSun). This work also represents a preparatory step in the application of a new bar-optimized stellar dynamical modeling code.