Ms1238, what exactly do you want your wearable fitness device to register when you're boxing?
Your Garmin wearable device has to be a model that supports tracking of intensity minutes as a feature, and then it will only do so if its built-in optical heart rate monitor (usually worn just above your wrist, although I suppose it could possibly work when the sensor is pressed against some other area of your skin) can detect your heart rate in conjunction with movement detected by the device's accelerometer. That's the technical aspect of it, as far as my understanding goes.
Now, if it's about “getting credit” for your “most vigorous exercise”, personally I think it's just not worth worrying about if it doesn't come readily with the way the device is designed to be worn (which you “can't” do while boxing). Obviously we disagree on that, and will never see eye to eye there.