If you want people to have the utmost respect for your language skills, don’t tell them something is of the upmost importance. When you’re talking about something you hold in high regard, it might seem natural to use a word with “up” in it. But “upmost” and “utmost” are not interchangeable.
“Utmost” originated as a synonym for “outermost,” and it’s still used to mean a distant point. It also means “of the greatest or highest degree, quantity, number, or amount” and is the word you’re looking for in phrases such as “utmost importance” and “utmost concern.” It can also be used as a noun, as in, “She’s doing her utmost to ensure the project is finished on time.”