Can I count on any type of support from Swica or will this all be out of pocket?
I have frozen embryos in NYC that I would like to transfer (and eventually use) now that I am in Switzerland.
Welcome to the Forum.
I don't see a reason for a health insurance company to pay for transferring embryos across country lines. That's an import-export issue. There is bound to be a lot of red tape related to laws in both countries, and I don't know whether Switzerland would even allow such an import.
A quick online search shows that there are companies specializing in transport, but to ship internationally could cost $1,000 or more.
As for having treatment after you're here, IVF is not covered under the basic health insurance. You'd almost certainly need the private insurance, if they cover it. A quick search of Swica's website doesn't mention IVF coverage, but that doesn't mean it isn't offered.
It may be possible to find a Swiss insurance that does private worldwide cover, and that might cover you to get treatment in the USA.
Personally, I'd not risk trying to transport my embryos across countries. Too much can go wrong. I'd go to where the embryos are. But that's just me.
Best of luck to you.
Edit to add: According to [this site](ttps://www.cpma.ch/en-us/Questions-about-fertility/Egg-donation-and-treatment-abroad) , donated eggs and embryos are forbidden by Swiss law. This leads me to believe importing embryos is probably forbidden or that you have to go through extra hoops to prove the embryos are biologically yours and not donated.