There's a simple solution to the non-words "umm" and "uhh" in public speaking: it is virtually impossible to "umm" and "uhh" when you are making eye contact with a specific person.
Umms and uhhs happen when you look at your notes, the wall, the ceiling, the floor, or a crowd. They never happen while you are looking directly at another person's eyes. Try it for yourself. Observe how people make eye contact when they speak, or don't, at the next meeting you attend.
If you're on the phone, and more importantly, when you are recording the call for subsequent distribution (and posterity!), look at a picture of a real person. (Caveat: make sure the person in the picture is someone who elicits appropriate vocabulary for the call. You don't want to accidentally slip into baby talk during a marketing presentation.) In a pinch, speaking to a drink bottle or a coffee cup, pretending it has eyes, will do, but a picture of a real person is better.
Dogs cooperate more than cats.
The first time you try to make eye contact with a real person when and every time you speak, your eyes will hurt by the end of the day. Then, you'll start noticing how few people make eye contact all the time.
Spread the word. Make eye contact when you do it.
We discovered this solution in Powerful, Persuasive Speaking, a two-day class presented by Alan Hoffler of Mills Wyck Communications. If being more persuasive would help you be more effective in your work or vocation, we cannot recommend this class enough. In my session, one professional (NSA) and one pretty good amateur speaker both observed marked improvement in delivery skills. People with no prior training in public speaking made amazing improvements.