I've had two separate occasions where Ward did not trigger upon casting a removal spell.

First occasion: Skyward Spider with Ward 2 and another Ward 2 from Sheltered By Ghosts. I have one of my opponent's Nowhere To Run exiled with seam rip. Opponent casts Wistfulness and taps out, removes Seam Rip. Nowhere to Run re-enters, targets my Skyward Spider, which dies. Ward 2 should have triggered and countered the -3/-3 since opponent could not pay the Ward cost.

Second occasion was similar: Creature with Ward and with a tapped-out opponent was targeted with Bitter Triumph and was still removed even though opponent was not able to pay Ward costs.

Platform: Steam on Win11.