Both Shimano SPD pedals on my Tour Easy have been creaking while climbing hills and I’ve gradually eliminated all the usual mechanical suspects: loose bottom bracket bearings (it’s a cartridge), loose cranks (they’re the old-school tapered squares), loose pedal spindles, and so forth. Of course, it’s impossible to produce the creak with the bike clamped in the work stand, which make debugging particularly frustrating.
After all that, I noticed the shoe soles were wearing the pedal frames just outside the cleat clamps:
So I went so far as to carve away a bit of the sole:
Turns out none of that solved the problem.
What did solve the problem: a drop of oil on the rear of the cleat. You can see a smear of oil on the sole; it doesn’t take quite so much.
As nearly as I can tell, the rear of the cleat drags on the slightly irregular surface of the clamp and, both surfaces being hardened steel, they stick-and-slip just slightly.
A dab of grease may provide longer-lasting relief …