In some ways, this really depends on the composition of the board of advisors, and might vary on a personal basis. Some will be motivated to participate on your board for reasons other than a financial reward, especially if they are part of a network that might derive value at a future date with any influence they have over your emerging business. That sounds abstract, so let me give you an example:
Lets say you have a company that is going to make a new process that could lower the costs of producing widget X, perhaps through some new material you've invented. You might seek out advisors from the industry that makes widget X, especially people who have connections that can evaluate and perhaps propose integrating your process into making widget X. This person might like a small stake in the company, but their prime motivation is that they could get a jump on the competitors by potentially using your product, perhaps on an exclusive basis.
So while you might go for a "take a small stake" approach, I really feel that gathering advisors that have other incentives that are tied to your success are going to produce much better results. Definitely compensate them for travel costs and make sure they're taken care of while they're at your meetings though, you do want to smooth away any barriers that would make them reluctant to meet.