How much does it cost to deal with there's a big broken branch hung up in my tree?

Priced on access and height rather than on the size of the branch. Reaching a hanger means getting a climber above it or a bucket alongside it, and the crew has to work around a piece that will move unpredictably the moment it is touched — short labor, but skilled labor. After-hours response costs more, and here that premium buys something real. Cost climbs sharply when the hanger sits over a roof or near a service drop, and anything touching or close to power lines is the utility's call before it is a tree service's, so call them first. Cleanup and haul-away of the branch itself is usually a small share of the total; the reach is what you are paying for.