The violation of charge conjugation (
C
) and parity (
P
) symmetries are a requirement for the observed dominance of matter over antimatter in the Universe. As an established effect of beyond the Standard Model physics, this could point towards additional
C
P
violation in the Higgs-gauge sector. The phenomenological footprint of the associated anomalous couplings can be small, and designing measurement strategies with the highest sensitivity is therefore of the utmost importance in order to maximize the discovery potential of the Large Hadron Collider. There are, however, very few measurements of
C
P
-sensitive observables in processes that probe the weak-boson self-interactions. In this article, we study the sensitivity to new sources of
C
P
violation for a range of experimentally accessible electroweak processes, including
W
γ
production,
W
W
production via photon fusion, electroweak
Z
j
j
production, electroweak
Z
Z
j
j
production, and electroweak
W
±
W
±
j
j
production. We study simple angular observables as well
C
P
-sensitive observables constructed using the outputs of machine-learning algorithms. We find that the machine-learning-constructed
C
P
-sensitive observables improve the sensitivity to
C
P
-violating effects by up to a factor of five, depending on the process. We also find that inclusive
W
γ
and electroweak
Z
j
j
production have the potential to set the best possible constraints on certain
C
P
-odd operators in the Higgs-gauge sector of dimension-six effective field theories
