When I connect the U2004A USB power meter to my device I get a low level power measurement, even when there is no RF applied …

The U2004A power sensor is DC coupled. Any low frequency low level signal on your device may appear as a low level signal. This may be due to a ground loop, leaking capacitor, bias signal, or other sources of low frequency or DC single. We recommend using a DC block or to perform a power sensor zero with the power sensor attached to the device.