wireless bluetooth headphones iphone 5 s case

I don't know how wireless on-ear headphones work. I was looking for wireless headphones because the jack on the wired Sennheiser headphones does not fit into the audio port of the iPhone 5s with the case on, and we would like to leave the case on the phone.

For wireless headphones, does something need to be inserted into the headphone port? If a "transmitter" needs to be inserted into the headphone port, does it fit with the Apple iPhone 5s case on?