And similarly, by testing them in the first place, you're telling them that they're not trustworthy.
Children have a remarkable ability to become what their parents tell them to be.
Do you want to tell them not to be trustworthy?
I wouldn't test my kids covertly. It would be very upfront, because I agree that being sneaky about it only lets them know that its OK to be sneaky. I would simply tell them that if they don't pee in a cup, I'll just get some of their hair from the hair brush.
drkitten, lets try a more concrete example:
drkitten enters her teenage daughter's room. The lights are out, and the kid is lying in her unmade bed. She is fully dressed in the same clothes she put on 3 days ago, and reeks of sweat and vomit, and drkitten also assumes that the urine smell is not from the dog. Drkitten reaches out and shakes her daughter gently, and the daughter shrieks, her eyes darting about the room as if something is about to jump out and attack her.
Drkitten: "Honey, I can't stand to see you like this. Please tell me what's wrong."
Kid: "Nothing, mom. I'm fine, leave me alone"
Drkitten: "It's obviously not nothing, honey. I'm really worried about you. You haven't eaten in 3 days. You haven't even come out of your room. Please tell me."
Kid: Sullen silence, then quiet tears.
Drkitten: "Honey, are you taking drugs, is that it?"
Kid: "No mom. It's nothing like that, I promise. I just can't tell you what's wrong."
Drkitten sighs and starts to pick up her daughter's room in what even to her is an obvious attempt to distract herself from her daughter's pain. She notices a corner of a ziploc bag sticking out from under the mattress, and pulls it out intending to throw it away with the rest of the trash. Inside the bag is a fine white powder and a glass pipe. Oh jeez, drugs!
Drkitten: "Honey, what is this?! Are you doing drugs?! Is this crank or crack or something?!"
Kid, highly agitated: "Give that back! You have no right to take that! I'm just holding it for someone else at school! Get out and leave me alone!!!"
Drkitten, knowing now that her daughter has a substance abuse problem, starts the ball rolling and for the next 6 months, her daughter is treated intensively as an outpatient by a psychiatrist. But her daughter is stubborn, and refuses to admit she has a drug problem, despite the obvious facts. However, she cannot or will not give any other reason for her obvious sudden deterioration. Then it becomes clear that her daughter is pregnant. It turns out that those drugs weren't her daughter's after all. She was holding them for a friend at school, just like she said. Her daughter actually had been raped by her boyfriend.
It really comes down to what you consider more important. Getting the right kind of help for your kid or maintaining their trust in you. The two may be mutually exclusive. I can hope to rebuild the trust, but my kid has to be alive to do it. You can't treat a problem effectively without knowing what the problem is. As egslim has pointed out, the kid could be going to hell for reasons other than drugs, so just assuming they have a drug problem without proof and directing your efforts toward that end would be worse than useless. If your kid had symptoms of a medical problem like diabetes, would you not demand a blood test even if the kid doesn't want one? If your kid was showing symptoms of a brain tumor that made him irrational, would you not insist on an MRI regardless what they thought or said? I don't really see the difference. Whether you consider drug use a purely psychological problem, or a medical disease, it shouldn't be treated any differently just because the kid doesn't want to admit to you that they have a problem.