We present the results from performing spectral energy distribution (SED) fitting on 121 variable active galactic nuclei (AGN) candidates in the Hubble Ultra Deep Field using photometry from both the Hubble Space Telescope and the James Webb Space Telescope (JWST) covering 0.2–4.8 μm. We designed a bespoke SED fitting code, which decomposes the total SED into its stellar and AGN contributions. Our SED fitting retrieves a significant contribution to the total SED from an AGN template for 26 of our variable sources with 0 < z < 7. We leverage the model AGN spectrum to estimate black hole masses (M_BH) using the measured luminosity at 5100 Å and local empirical calibrations. Common with recently discovered JWST broad-line AGN, we observe a trend in the M_BH–M_* plane where low-redshift sources have M_BH that agrees with local relations while high-redshift sources have increasingly overmassive black holes with respect to the stellar mass (M_*) of their host galaxies. Within our sample, we identify two IMBH candidates hosted by dwarf galaxies at z < 1 featuring overmassive black holes in the M_BH–M_* plane, similarly to our high-redshift sources. Finally, our SED fitter successfully retrieves the AGN nature of one source at z > 6. This object has z_phot = 6.74, and we estimate a lower limit on its black hole mass of log₁₀(M_BH/M_☉) > 7.36.