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The complex surface impedance of a superconductor provides many insights into its properties, such as the pairing mechanism, super- and normal-fluid responses, Fermi surface, and possibly it’s topological properties. We explore the surface impedance of UTe₂ single crystals as a function of temperature using resonant cavity measurements for a variety of microwave-frequency modes. We determine a composite surface impedance for each mode using resonance data combined with the independently measured normal state dc resistivity tensor. We can determine the combination of crystallographic directions excited in each mode and the surface impedance corresponding to each axis using the anisotropy of the resistivity. We compare these results with those of NbSe₂, a conventional but anisotropic superconductor. For UTe₂, we find approximately a T² power-law dependence for the magnetic penetration depth in both the a- and c-directions, which is inconsistent with a single pair of point nodes on the Fermi surface. We find the zero temperature penetration depth to be largest for the c-direction, which is consistent with the current understanding of the Fermi surface shape. The surface resistance demonstrates a relatively large residual loss at zero temperature, and the c-direction is the most lossy.