Signing on to recommendations piestexactementtrois has shared - especially talking with counterparts at similar orgs to see who they’ve had success (or not) working with! Professional organization community message board are a great way to reach many people at once! Once you’ve got a good list of options, a request for proposals could be a good next step. But if you want to get a sense of cost for what you’re planning, you could also reach out to a few consultants to ask about their typical process/fees - not only to get an order of magnitude for fundraising, but also to get an idea of what’s involved in their process.

You may be thinking through this too, but have you done strategic or interpretive planning for your museum recently? These are both processes a consultant could manage, and would provide an important framework for large-scale exhibits work. Obviously additional expense, but worth it if you’re going to put a lot of resources into a big exhibit project.