We quantified and calibrated the metallicity and temperature sensitivities of colors derived from nine Wide-Field Camera 3 filters on board the Hubble Space Telescope using Dartmouth isochrones and Kurucz atmosphere models. The theoretical isochrone colors were tested and calibrated against observations of five well studied galactic clusters, M92, NGC 6752, NGC 104, NGC 5927, and NGC 6791, all of which have spectroscopically determined metallicities spanning -2.30 < [Fe/H] <+0.4. We found empirical corrections to the Dartmouth isochrone grid for each of the following color-magnitude diagrams (CMDs): (F555W-F814W, F814W), (F336W-F555W, F814W), (F390M-F555W, F814W), and (F390W-F555W, F814W). Using empirical corrections, we tested the accuracy and spread of the photometric metallicities assigned from CMDs and color-color diagrams (which are necessary to break the age-metallicity degeneracy). Testing three color-color diagrams [(F336W-F555W),(F390M-F555W),(F390W-F555W), versus (F555W-F814W)], we found the colors (F390M-F555W) and (F390W-F555W) to be the best suited to measure photometric metallicities. The color (F390W-F555W) requires much less integration time, but generally produces wider metallicity distributions and, at very low metallicity, the metallicity distribution function (MDF) from (F390W-F555W) is ~60% wider than that from (F390M-F555W). Using the calibrated isochrones, we recovered the overall cluster metallicity to within ~0.1 dex in [Fe/H] when using CMDs (i.e., when the distance, reddening, and ages are approximately known). The measured MDF from color-color diagrams shows that this method measures metallicities of stellar clusters of unknown age and metallicity with an accuracy of ~0.2-0.5 dex using F336W-F555W, ~0.15-0.25 dex using F390M-F555W, and ~0.2-0.4 dex with F390W-F555W, with the larger uncertainty pertaining to the lowest metallicity range.Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with program 11729 and 11664.