After looking at the 7937 product data sheet it noted that the phone supports "a third-party lapel microphone kit". I assumed this was a Polycom product since the Cisco conference phones are made by Polycom.
I received it this morning and it's pretty straightforward to put together. It consists of a transmitter with a lapel microphone that takes a 9V battery and a receiver with an RCA connection and antenna. The problem at this point is getting the RCA connection into the 7937 phone.
The phone contains two types of microphone inputs. One of the inputs is a proprietary Cisco connection for two wired mics. We didn't purchase these as it was an additional expense and when we've purchased them in the past on the 7936 phone we ended up not using them. It wouldn't really help in this situation anyway.
The other option was a 3/32" jack similar to what's on some cell phones. This was hidden behind a door on the bottom side of the phone and had some obscure drawings next to it trying to explain what it's for. The best I can tell is the drawing is trying to illustrate that this jack could be used for input or output, but I haven't tested the output portion or found any documentation on it.
To get the RCA connector to plug into the 3/32" jack I headed over to Radio Shack. Unfortunately they didn't have a converter that would convert RCA to 3/32" so I had to get two converters. I'm going from RCA to 1/8" and then from 1/8" to 3/32". I'm sure if I had more time I could have ordered a cable that would have 1/8" on one end and 3/32" on the other end so I wouldn't need any converters and wouldn't have to use the RCA connector that came with the microphone. Since the converters were under $10 I decided to go ahead and try this route. Maybe down the road I'll get a cable so we don't have to worry with losing these adapters.
I connected all the adapters up and plugged in the receiver. I clipped the transmitter to my belt and clipped the lapel mic to my collar. I placed a call to my coworker and it worked! He could hear me loud and clear. I went for a walk around our floor, out to the break room, and into a wiring closet. He could hear me the entire time even though the antenna on the receiver wasn't even extended. Also, I didn't have to look down at the microphone. Just talking with my head held normally he could hear me great.
If anyone from Cisco or Polycom is reading this, the Polycom wireless lapel mic (Part #2200-00699-001) does work with the 7937. It doesn't directly connect, but after an RCA to 3/32" jack adapter you're in business.