Let Others Speak For You
Some people will write an endorsement, but many prefer you to give them a suggested paragraph that they can (but often won't) edit. That's where your earlier work comes in handy. Using words that came right from their mouths establishes a level of comfort and often minimizes editing. Be realistic, though; you're more likely to get someone to agree to say you are a good organization that is worthy of support, than that you are the best organization in the entire universe and only a fool wouldn't support you.
Use terms and phrases that the person normally uses. Capturing his or her pattern of speech leads to the feeling that "This is exactly what I would say." One of the "highs" for me was hearing a major celebrity endorse an organization using the exact words I had written; it was obvious I had captured his voice and the nuances of his speech.
Ask, thank, ask again.
Once you have written or extrapolated an endorsement, ask permission to use it. Then ask again every so often, perhaps with an updated version if desired. Don't just assume that saying "yes" now is a blanket approval for the rest of time.
Treat your endorser like you do a donor; send an appreciation letter from time to time, and if you send out a calendar or another small token gift, make sure your endorsers get one with a personal note of gratitude. This helps keep the bond they feel with your organization strong, and will help you stay top-of-mind throughout the year.
Having more endorsements than you can use at any one time is a terrific problem to have. Even a non-famous person can be a great endorsement in the right circumstance (for example, to confirm that your work is best practice in a particular field), so cast your net wide.