I have never used invisible fencing, and will not recommend it to anyone. Invisible fencing is contraindicated for boxers, because of the following, as eloquently put by breeder Theresa Garton, of Oklahoma:
"Boxers are stoic about pain. I tried regular electric fencing once, to back up an area of my stockade fencing I was having problems with. The bitch that was getting out of this area definitely felt the pain, I saw her jump straight up many times as she touched it. She STILL wouldn't leave it alone, and tested the wire all up and down the length of it. She didn't go through the hole I couldn't seem to fill for about a day, and then, I guess she decided the shock was worth the fun of getting through to the other side. She apparently would just grit her teeth and hurry. "
I also put electric fencing around the top of my 6 ft wooden fence, as my smallest bitch was escaping. I watched her one day bounce high enough to catch her front legs on the top and she then pulled herself over. After installing the electric fence, I watched her pull her trick again. The electric fence shocked her (in more ways than just physically), but didn't deter her from trying again and again to jump over. As stated above, she determined that the fleeting pain was worth the thrill she found on the outside of the fencing.
The signal is temporary and fleeting. If the dog has momentum (and/or motivation- see above) as they are running the line, they can miss the signal, end up on the other side of the electric fencing, and then not be able to get back in without receiving a shock.
Electric fencing doesn't keep other dogs (animals) out of your yard. This means aggressive dogs can still come in and challenge your Boxer, and smaller dogs can come in and be injured, with resulting problems with neighborly relations.
The fence only works if you are absolutely sure your batteries are fresh and working.
The flags used to train for the invisible fencing are similar to those used in tracking to mark the trail during training. It has been reported that some dogs show fear of the tracking flags because they have electric fencing at home.
In summary, invisible/electronic fencing is not recommended for boxers (or any pet really). Regular physical barrier fencing protects your dog and your property by keeping him in and everyone else out.
Do not leave your dog unattended outside for long periods, regardless of your containment system. Even in my rural area there are reports of missing/stolen dogs--the only common denominator was that they were left outside unattended.