When we use an auxiliary verb without any other verbs or complements, we say that that auxiliary verb has been STRANDED. This is usually because we know the listener can userstand what other parts of the verb phrase are missing:
- Can you open it?
- Yes, I can! [means "Yes, I can open it"]
Sometimes it is because the complements of the verb have been preposed. This is normally because they are part of a wh- phrase that has moved to the front of the sentence. This is what has happened in the Original Poster's example, where the wh- phrase has moved to the front of the exclamative clause:
- I can't tell you how excited I am [
When an auxiliary is stranded it must have its strong form. That means it must have a full vowel. Often, but not always, it will be stressed. We can't contract pronouns with auxiliary verbs if the auxiliary has a strong form.
- Are you listening?
- *Yes, I'm (X)
- Yes, I am (grammatical)
Edit note: As noted by Ben Kovitz, the verb have doesn't always seem to have a strong form when stranded after a modal verb: /hi kʊd əv/. I don't know why this is, though. And I've never found anyone who does!
Hope this is helpful!