Police at a checkpoint detected a smell of cannabis when they stopped a car in the Ballinderry area, a court has heard.
Andrew Wallace (26), of Letteran Road, Cookstown, was fined £200 with a £15 offender levy for possessing the drug on July 12 last.
Jennifer Montgomery (27), Windsor Terrace, Coagh, was fined £175 with a £15 offender levy for the same charge.
Imposing the fines, District Judge Michael Ranaghan expressed the hope that the defendants had now finished with drugs as they would not be fined if they appeared in court again.
Prosecution counsel told Dungannon Magistrates Court that when police stopped the vehicle, Wallace admitted he had been smoking cannabis.
He explained that a search was carried out in which traces of the drug were found in a pocket of the vehicle.
Counsel said a small quantity of the drug was also found in a jacket pocket of Montgomery who was driving the vehicle.
He described the amounts of cannabis as small and there was no indication as to its value.
Defence solicitor Stephen Atherton asked the court to give the defendants credit for their early pleas.
Mr Atherton said they had been taking the drug for medicinal reasons but had now stopped taking it. He stressed both had admitted their guilt to police.
The judge made a destruction order in respect of the cannabis seized.