Though there is a science (of sorts) of responding to objections,  usually the best is simply  getting the person talking.  Listen, explore what is behind the objection (or their hesitation, even if it is not a clear objection).  Then, when you have a sense of what is bothering them, respond accordingly.

Suppose you've arrived for your sales appointment, and now the prospect is saying something to the effect, "Sorry, I don't want to keep this meeting with you, after all." 

You could respond, "Why not?"  That might be okay, but it might also be perceived as confrontational.

A better probe to get them talking:  "When you say that you don't have time to talk, do you mean just as the moment?" Pause to listen to their response.  Then: "Perhaps we could reschedule for some time next week, perhaps on Monday afternoon? Or would Thursday morning be better for you?" 

Second probe, if necessary:  "You say that you don't feel our meeting would be a good use of time.  Why do you feel that way?"

Third probe: "When we talked on the phone last week, you seemed quite interested in discussing the possibilities, particularly given (my firm's) record of success with other firms in the area."   (If you had made that call on the basis of a referral from another client, remind of that name at this point.) "Has there been a change since then?"