Much of New England has experienced severe drought this past summer so the dead-looking brown branches may reflect lack of sufficient water. It's not too late to give the ground a good soaking if it still seems dry. There are also serious fungal infections of the roots which can also cause the dieback of individual branches and entire plants. With the onset of colder weather these pathogens become inactive so damage has ended for this year. Drought damage is probably much more likely than fungal infection unless you were diligent in keeping these watered.

Best thing to do is nothing until spring. You may see swelling buds on some of the branches which now look brown and droopy. If you still see lots of dead looking branches after the rhododendron blooms, prune them out. There will be plenty of time for regrowth.

Yes if not drought then root or stem rot due to water molds. Damage from these is common on rhododendrons and related plants.

I would water the soil deeply to provide needed moisture and then I would add 3-4" of mulch to maintain the soil moist longer and protect the roots in the summer/winter. Try to keep the soil as evenly moist (not wet) as you can. Due to lack of rain, take advantage of rainfall and do not water if it has rained. Too much water (meaning the soil feels wet) is not good so do not go overboard watering.

If it helps you, try a soil moisture meter or water the soil (not the leaves) only when a finger inserted to a depth of 4" (not counting the mulch) feels almost dry or dry. Water from the rootball outwards.

The first time you water after posting this, feel free to water more than usual (one-time only) as the soil is playing catch up with the amt of water provided. Pay special attention to watering around the rootball. Usually this is done by watering a trickle (one slow drop at a time from a hose) for about an hour. The rootball if it has dried, will repel water so extremely slow watering is needed to get it absorbing again. Away from the rootball, the tiny fibrous roots near the top 4" are the ones that absorb water so get those moist too. They will not need the slow drip method that the rootball needs though.

Looks like classic Botryosphaeria. It is a fungal disorder but not easily treated with fungicides. To confirm, cut one of the affected branches to see if the wood is reddish brown on one side.

I have never seen drought symptoms on rhodies manifest in this manner. It is more of an overall droopiness and lack of vigor that indicates water stress, not a complete die back of individual branches here and there. That looks to me very much like a fungal issue or root rot. I would recommend removal of any obviously browned or dead branches - they are not going to regenerate into a healthy branch! And I would also say the prognostication for a good outcome for the remaining plant(s) is iffy at best.

Drought stressed plants on the east coast tend to be more susceptible to fungal infections. Which was probably the sequence of events that occurred with a rhododendron that presumably, was healthy before this summer.

"Looks like classic Botryosphaeria"

Just looked at your profile because I hadn't seen your name before. You're from Christchurch, NZ. A bit to my surprise, a few of the plants at the Ilam Gardens had this sort of dieback.