If there were a surefire way to beat a ticket someone would be rich. The only way to "beat" a ticket is to not get them and this is done best by not speeding. Whether or not you will be found not responsible will be based on what speed statute you have allegedly violated, what evidence the police department/officer presents, what evidence you present, and whether the police department meets its burden of proof (i.e. that you were more likely than not speeding).
Depending on what is at stake (license loss, insurance surcharge) you may wish to consider hiring an attorney to represent you, or hiring an attorney to explain the process, the standard, and what to expect.
DISCLAIMER: This answer is provided in response to a "hypothetical" question and provided for general, informational purposes and does not create an attorney/client relationship. The information presented is not legal advice and may change based additional information and research. It is recommended that you speak to an attorney to discuss your specific legal issues.
Over the past few months, I have represented four different clients in your situation and prevailed in each case. For some success stories check out the "recent results" section of my website at www.thecriminaltrialattorney.com. Feel free to call me at 774 254 4411. In order to be found "not responsible" of your speeding ticket, the most important factor is knowing what to say and what not to say to a clerk magistrate and/or a judge if it goes all the way to the appellate level.
Basically, the officer will need to show he followed behind you for a period, watching his speedometer (this is the clocking aspect of the ticket). The estimated means that he visually estimated you were traveling faster than the posted speed limit. The officers almost always check off estimated, and it bears little weight in the hearing.
What you really need to establish is that a) there was other traffic on the road and the officer clocked the wrong vehicle or b) the the officer's equipment was properly calibrated and therefore is unreliable. Because it is clocking, it is the least reliable measurement of speed.
If you would like to discuss this matter further or would like to inquire about representation, please feel free to contact me directly.
Kelly A. Broadbent
Nelson & Broadbent
160 Doyle Road
Holden, MA 01520