can a search be conducted with a warrant?
Yes, Under the Fourth Amendment, law enforcement must receive written permission from a court of law, or otherwise qualified magistrate.
Fourth Amendment to the United States Constitution
Under the Fourth Amendment, law enforcement must receive written permission from a court of law, or otherwise qualified magistrate, to lawfully search and seize evidence while investigating criminal activity. 
what is the fourth amendment to the united states constitution? It is a part of the Bill of Rights. It prohibits unreasonable searches and seizures. when was it introduced? 1914 do you know by whom? UNANSWERABLE are there exceptions? Yes,  In "United States v. Martinez-Fuerte" (1976), the Supreme Court allowed discretionless immigration checkpoints. In "Michigan Dept. of State Police v. Sitz" (1990), the Supreme Court allowed discretionless sobriety checkpoints. In "Illinois v. Lidster" (2004), the Supreme Court allowed focused informational checkpoints. does it include cars? No,  The Supreme Court has held that individuals in automobiles have a reduced expectation of privacy, because (1) vehicles generally do not serve as residences or repositories of personal effects what are the limitations? UNANSWERABLE
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Fourth Amendment to the United States Constitution [SEP] Warrant
Under the Fourth Amendment, law enforcement must receive written permission from a court of law, or otherwise qualified magistrate, to lawfully search and seize evidence while investigating criminal activity. A court grants permission by issuing a writ known as a warrant. A search or seizure is generally unreasonable and unconstitutional if conducted without a valid warrant and the police must obtain a warrant whenever practicable. Searches and seizures without a warrant are not considered unreasonable if one of the specifically established and well-delineated exceptions to the warrant requirement applies. These exceptions apply "[o]nly in those exceptional circumstances in which special needs, beyond the normal need for law enforcement, make the warrant and probable cause requirement impracticable".