It has been awhile since I handled a case of this type, but I will endeavor to set out the law, as best I can recall, on airport searches. Airport searches are administrative searches and are an exception to the Fourth Amendment's warrant requirement. The search must be designed to further a manifestly important governmental interest under circumstances where the program is reasonably tailored to further the governmental interest and where the intrusion on personal privacy or security is relatively slight in comparison to the interest served by the program. Further, those who are the subjects of an administrative search must consent to the search. Consent is typically implied. There is a sign posted warning you of the search, you pass the sign, you have consented to the search. You are free at any time prior to undergoing the search to return to your car and drop off your pocket knife. Once the search commences, you have consented to the process and it is reasonable to allow the process to run its full course.
Assuming the authorities have seized your pocket knife or multitool, you probably have little in the way of recourse, including under the Just Compensation Clause of the Fifth Amendment. You are entering a sterile area and edged weapons and tools have been deemed to be either contraband or dangerous or deadly weapons. Either way, you are not allowed to have them in sterile areas and so you have probably forfeited your property rights.
atty_guy