How is the DC voltage offset measured in a microwave circuit? Is a super expensive oscilloscope needed? Thanks.
No, you can use any oscilloscope for that.
Since you're needs just DC component, oscilloscope bandwidth doesn't matter.
Also you can use DMM, and even cheap one like Chinese DT830
The possible issue with DMM is that it's probe impedance on a microwave frequency can affect your microwave circuit mode. If it's not an issue for your microwave circuit, then you can use usual DMM in DC mode.
Just switch your DMM to DC Voltage mode and connect it's probes. It will show you DC offset, because microwave frequency will be cutoff with a low input bandwidth of the DMM.
But be careful, if your microwave circuit has a high amplitude/power output you can damage your DMM or a power amplifier of your microwave circuit. You can use it for low power RF output. For a high power signal you can use RF inductor to feed your DMM with DC component. But don't forget to attach proper load for your signal source and use proper soldering for inductor to avoid impedance issues - don't use wires, solder one pin of the inductor into transmission line directly.
For example I'm using my Brymen BM867S in DC Voltage mode to measure DC offset at 10-400 MHz. And it works ok.
PS: just tested my BM867 DMM and it works ok from 20 Hz, but the lowest frequency limit will depends on DMM type.