Tantrums are a recipe for a disaster for highly sensitive parents. And while I know some parents prefer to walk away for a bit while their child works it out (HSP or not, tantrums grate on many people's nerves), that never worked for me. It made me too anxious and I didn't feel that it was helping my daughter.
Instead, I've put a lot of time and effort into modelling and teaching self-calming skills. I started by using time-ins whenever she started to lose control, where I'd model how to take deep breaths and deal with her emotional state first before addressing the rational part of the issue.
Because my daughter is well-versed in regaining her composure and finding the words to express herself effectively, even though she inevitably has tantrums, they are not long and drawn out.