Pronunciation for advanced learners

Most of my students are advanced. Most have a very good grasp of English pronunciation of individual words. But where most, if not all, struggle to sound natural - is when it comes to sentence stress and intonation.
Yes, individual words have syllable stress, which is important. But beyond single words, there is a kind of musicality to whole sentences in English, which have stress patterns of their own, according to what the sentence - as a whole - is conveying. Most learners of English tend to focus on pronouncing each word separately and clearly, but do not pay enough attention to how the sentence as a whole unit of information should be pronounced, in order to communicate the intended meaning. The result is that it can be harder for a listener to follow and immediately recognise the intended meaning, if the speaker's intonation does not flow in the usual or expected manner. It can be difficult initially for learners to create stress patterns with their voices but certain exercises can help with this, which, once you get the hang of it, will help you sound much more fluent, amazingly quickly.
On my recent course, some of the tutor feedback I received was that I needed to focus more on whole sentence pronunciation with students - and I've been implementing this with many of my regulars, with brilliant results! For example, working on a sales pitch with a long-term regular, we have carefully analysed which words in her presentation sentences are most important, and need to be given the most 'weight' as it were - then, we have drilled those sentences, using bold and caps as visual text guides to how to say them, in order to professionally convey the intended meaning. Soon, she'll be recording her pitch to send as a video message to prospective clients.
Sometimes, to show students how important sentence stress is for effective communication, I give them the example of a simple one word sentence said in three different ways - and it always makes people laugh! Try to imagine these in your 'mind's ear': "Hello?" with a rising inflection means, "Who is this?" - the kind of 'hello' we usually hear on the 'phone. "Hello!" with an exclamation probably means something like, "Hi! Good to see you!" - indicating we are happy to see that person. "Hello." with a falling inflection might mean, "Oh, you're here." - possibly indicating we are, in some way, annoyed with that person.
Usually, it is fairly easy to ascertain which words are the most important in a given sentence, and therefore which should be stressed. But of course, language is infinitely flexible, and we can vary the stress precisely in order to deliberately change the meaning.
Let's consider the following sentence as an example:
I said I want pizza for dinner.
It could be said without any particular stress at all, as in reporting an interaction from the past. But notice what happens if we choose to stress one word:
I said I want pizza for dinner.
I said it, not someone else.
I said I want pizza for dinner.
Didn't you understand me?
I said I want pizza for dinner.
I want pizza, not someone else.
I said I want pizza for dinner.
I want pizza, not anything else.
I said I want pizza for dinner.
I want pizza for dinner, not lunch.
Try saying the above in all the different ways, using your voice to communicate the difference in meaning.
Another helpful exercise and one which I've been doing more often lately, is to record a few key phrases or sentences at the end of the class - then, I send the audio link after the end of the lesson, so my students can keep practising using the audio file. This is useful for word and sentence 'shadowing', whereby you try to copy the intonation exactly, and again - can really help boost your confidence to have a reference for phrases you repeatedly need to use in your real life!