We present the detection of supermassive black holes (BHs) in two Virgo ultracompact dwarf galaxies (UCDs), VUCD3 and M59cO. We use adaptive optics assisted data from the Gemini/NIFS instrument to derive radial velocity dispersion profiles for both objects. Mass models for the two UCDs are created using multi-band Hubble Space Telescope (HST) imaging, including the modeling of mild color gradients seen in both objects. We then find a best-fit stellar mass-to-light ratio ($M/L$) and BH mass by combining the kinematic data and the deprojected stellar mass profile using Jeans Anisotropic Models (JAM). Assuming axisymmetric isotropic Jeans models, we detect BHs in both objects with masses of $4.4^{+2.5}_{-3.0} times 10^6$ $M_{odot}$ in VUCD3 and $5.8^{+2.5}_{-2.8} times 10^6$ $M_{odot}$ in M59cO (3$sigma$ uncertainties). The BH mass is degenerate with the anisotropy parameter, $beta_z$; for the data to be consistent with no BH requires $beta_z = 0.4$ and $beta_z = 0.6$ for VUCD3 and M59cO, respectively. Comparing these values with nuclear star clusters shows that while it is possible that these UCDs are highly radially anisotropic, it seems unlikely. These detections constitute the second and third UCDs known to host supermassive BHs. They both have a high fraction of their total mass in their BH; $sim$13% for VUCD3 and $sim$18% for M59cO. They also have low best-fit stellar $M/L$s, supporting the proposed scenario that most massive UCDs host high mass fraction BHs. The properties of the BHs and UCDs are consistent with both objects being the tidally stripped remnants of $sim$10$^9$ M$_odot$ galaxies.
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