We use a variant of the surface brightness fluctuations (SBF) method to study the globular cluster populations around NGC 4874 and NGC 4889 in the I band. The fluctuations due to globular clusters, a nuisance factor in the standard SBF technique, provide a means for investigating that portion of the globular cluster population which cannot be observed directly. At the distance of Coma, we can also directly count the number of clusters occupying the bright end of the globular cluster luminosity function (GCLF). The direct counting and fluctuation measurements together provide a constraint on the width of the GCLF, which in turn decreases the uncertainty in the inferred specific frequencies. We find the Gaussian widths of the luminosity functions to be 1.43 +/- 0.09 mag and 1.37 +/- 0.13 mag for NGC 4874 and NGC 4889, respectively, Using these measured Gaussian widths, we derive specific frequencies (S-N; number of globular clusters per M(V) = -15 of galaxy luminosity) of 14.3 +/- 3.3 for NGC 4874 and 6.9 +/- 1.8 for NGC 4889, confirming that NGC 4874 is a member of the class of anomalously high S, galaxies. By measuring the globular cluster fluctuations at several radii, we find that S, increases outward from the centers of both galaxies, indicating that the globular cluster systems are more extended than the halo light, in accord with previous studies of NGC 4874 and nearby ellipticals. We confirm the reliability of our technique for measuring GCLF widths by applying it to NGC 4472 (M49) and NGC 4486 (M87) in Virgo. A brief discussion of the universality of the GCLF width for large ellipticals and the high S-N anomaly of central galaxies is provided.