A technique that many groups use to bring us into the present is a focus on body sensations. This is often used in meditation and in grounding techniques to help us get "out of our minds and into our bodies".
First, let's look at what this accomplishes and why it works. Our minds are often very busy dealing in concepts, theories, thoughts, opinions, and stories. All of these things can be very vivid - we can sit and imagine we are having a conversation with our boss, and feel like we are actually there so vividly that we completely disconnect from the room in which we are sitting and imagining.
A focus on body sensation brings us back to the current moment because, unlike our stories about the world, our body sensations change from moment to moment; and the only way we can tell what we are currently feeling is to stop thinking and "listen". That is the very attitude we need to be present. The importance is not what our body is feeling, although that may carry useful information. It is not critical to notice you have a tightness in your stomach, or a lightness in your head. It *is* critical that we are able to switch from our minds to "listening" to the current moment, and attention to body sensations is simply a technique to aid us in that switch. It may be much more critical, for example, to be noticing the body language and tone of voice of our boss when we are standing in front of him negotiating, than to notice our own body sensations. The point is to be present, not just to notice body sensations.
When our purpose is to connect to others, the practice of focusing on body sensations is not a big aid. If you are talking with someone you are trying to understand more, the goal of connection is not necessarily aided by you saying, "I notice that a tension is building in my chest as I talk to you." In fact, it could be taken as an accusation by someone not understanding what you are doing. The purpose of noticing body sensation is to privately make you more present, so that you can turn your focus on connection rather than on your internal process.
So a scenario might be this: I find myself arguing with someone I want to be connecting with. I look inside and notice that I am focused on concepts, on defending ego, on opinions and being right. To break myself out of that space, I take a silent moment to notice my body sensations, breathing, and stance. That causes me to let go of the grip of monkey chatter, and maybe give me some information about the physical and emotional state I am in. Now that I am listening to what is actually present, instead of my thoughts, I may notice we are both struggling with ego and trying to stay grounded. The result may be that I suggest we stop for a minute, go outside, and walk around, or do something else to facilitate the goal of a deeper connection. It is not about revealing my body awareness to the other person; it is about bringing myself into the present so that I can make better choices as to my words and actions.