Switzerland's major cities — Zurich, Geneva, Basel, Bern and Lausanne among them — all have access to round-the-clock veterinary emergency care, either through a dedicated 24-hour clinic or a hospital-affiliated emergency service that a regular vet will refer you to after hours.
In smaller towns and alpine resort areas, round-the-clock coverage is less certain, and the regional on-call rota (see Emergency Vets) becomes the more relevant system — ask locally as soon as you arrive rather than searching mid-emergency.
Given Switzerland's excellent but expensive veterinary care, it's worth having a payment method ready that works smoothly for a larger, unplanned charge — some clinics expect payment at the time of treatment rather than billing later.