Seems odd I know. But when a prospective client selects another firm over yours for a matter, rather than moving on immediately to something else, take a few moments to thank the prospect for the opportunity to make a proposal or for just being considered. You can do so by replying to the email, voicemail, or letter containing the rejection. It does two things, it shows you have class and if buyer remorse sets in and/or the services provided by the winner are less than the client expects, then you may very well get the next matter.
I also recommend that when you call the prospect to thank them (which is the preferred method), you also ask them what you could have done better with your proposal. You don’t want to come across as challenging their decision or trying to change their mind, you should make it very clear that you are merely trying to learn how you could do better in the future. In my experience, most will be willing to share some insight that will improve your future proposals.
John Jantsch further suggests when thanking the prospect when turned down, that you send an article or something helpful dealing with the issue for which you were trying to get hired. As he says it could be the start of your next pitch to this potential client.