The only watches I have seen have problems through airport security are vintage watches with steel hairsprings. Anything since the 60s should be fine.
Whether it’s an off-the-shelf ETA movement, a more advanced in-house mechanical movement, or a fully anti-magnetic METAS-certified movement — materials such as Nivarox (metallic alloy) or silicon (non-metallic) are used in all modern watch movements, and therefore going through security should not negatively affect timekeeping.