I get a clicking sound every time I go uphill, sometimes I can even feel it. It's coming from somewhere around the handlebar. I keep thinking that my handlebar might be cracking but its just my imagination.
I had a very similar "popping/cracking" sound coming from the handlebar/headset area of my '84 Schwinn Le Tour Luxe when I pressed on the handlebars. This is the bike that I still regularly use for my 10 mile round trip commute between home and work.
It took me a while to isolate from where it was coming, which was pretty annoying (I thought the problem was in the head tube). But I just figured out before my ride this morning that the noise was being caused by some grime/dirt/rust on the bolt used for tightening the handlebar clamp.
I took out the bolt and sprayed it with WD-40, then wiped it as clean as I could with a paper towel (but left a thin film of the WD-40 in-between the threads on the bolt). I then put the bolt back into the clamp and tightened it, and voila! there is absolutely NO noise anymore when I put pressure on my handlebars.
Hope this trick works for you (or future visitors to this blog who have the problem)!
When riding uphill you are putting more force on the bars to counteract the greater force you legs have to exert on the pedals.
What is probably happening is when you exert more force the handlebar or steerer tube is shifting in the stem clamps slightly, causing a creak or click.
Your stem clamp bolts should be tightened to the correct maximum torque. If that does not fix the problem the stem may need dissembling and re-assembling with some grease or assembly compound.