I have a number of trans woman friends who have shopped for women's clothing while still being male-presenting.
One important thing, as I think you've realized, is not to be too enthusiastic towards them -- treat them as you would any other (female-presenting) customer. If you start telling them how happy or excited you are for them, that's probably just going to make them feel more alienated.
If they start expressing doubts, feel free to reassure them, but don't go over the top.
Asking "how can I help you" rather than "who are you shopping for" is a great step as well.
Editing to add more detail about my experiences, as requested:
When I've gone shopping with my friends, the salespeople have mostly left us alone, which was fine by us.
I've also had conversations with several of my trans friends where they emphasized how uncomfortable they feel when people give them extra attention while trying to be supportive -- for example, giving them a big smile while on the bus. It reminds them that they don't "pass" as their gender, i.e. they "look trans". It makes them feel awful to be treated differently, even though the intention is good.