One great way to do that is to release early and often, allowing stakeholders to change plans in response to what they've learned. Instead of doing the work of (re-)estimating a bunch of stuff every week, their focus on what's actually going on lets them stop obsessing about arbitrary dates and semi-fictional plans.
People very rarely need estimates. They want a sense of control. They want to manage risk. They want to convince people that money is being well spent. They want to avoid looking like fools. If you solve those problems without using estimates, people generally stop caring.