In my view quite a few things make the connection, and determine whether it is a quality connection or not. Content. Conviction. Tone and volume of voice. Emphases. Humour. Timely shutting up. Pauses. But perhaps primary is our own connection with God. (How do we make a quality connection with the Unseen Presence at every service?).
Pretty much everything in the above paragraph can be 'worked on'. Improvement possible with training and with experience-from-which-we-learn-in-an-action-reflection-process. But there is another factor in making quality connection. If sticking with 'c' words then it is 'charisma'. We might also call it the 'x' factor, the factor in this context which means that we feel 'xtra' good about the way she or he leads a service or preaches a sermon compared to another leader or preacher.
Can we find the 'x' factor for ourselves if we do not already have it?
I am certainly open to arguments and evidences one way or another, but I think we can find it: seek it from God as a gift; ask God to work on things in our lives which are militating against it (such as, just one example, our insecurities); look for it to grow in us through experience; discipline ourselves to cut out what inhibits the x factor (e.g. self-put downs - a custom Kiwis acquire culturally?).