Picking up any signal is out of question. However, if you are a
paranoid suspecting someone is out to get you by recording, try this
one:
When she gets in your room/office, sing some line of song, like,
"Hellooo, is it me you're looking for? I can see in your eyes..." etc.
Stop kind of suddenly, look at her in the eye, and say, "If someone
recorded that song wouldn't it play back real nice?" She'll know you'd
caught her at her game and would blush or tremble or something.

Joey wrote:
Suppose someone visited your office or home and tried to make a voice
recording using a hidden recorder.

If they used a older-style dictation machine based on tape then you
could detect the electromagnetic transmissions from the dictation
machine when it was recording.

But how would you detect if someone was secretly recording with an MP3
player that recorded to flash memory?

Is there some transmission which could be detected?
Perhaps some low power ultra high frequency from chip refresh cycles?