We do sense the presence and moving of the Spirit in our meetings. In fact, we consider that there is something wrong if we don't sense the Spirit in a meeting. The reason we can be so definite about this matter is that endeavor to practice to worship God according to His word in John 4:24, "God is Spirit and those who worship Him must worship in spirit and in truthfulness." I think all believers should know that God is Spirit; that is the first Spirit in this verse, i.e. the one with the capital "S". But the second time the word "spirit" occurs in this verse it has a small "s" indicating our human spirit.
When God created man He formed a spirit within him (Zech. 12:1). It is in our spirit that the Lord dwells within us (2 Cor. 13:5, 2 Tim. 4:22). When we are joined to the Lord through regeneration we are even made one spirit with Him (1 Cor. 6:17). Thus, to sense the Spirit the most straightforward way is to exercise our human spirit. Our human spirit is the deepest part of our being so it can be very mysterious but when we open to the Lord with our whole being, spontaneously our spirit is also exercised. So when we pray, sing, or read the Bible we like to do it with our whole being, not just our mind or emotions. This enables us to touch our spirit and thus to sense the living, moving, shining, and speaking of the Holy Spirit.