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Altium can do that sort of thing fairly easily. We use it for boards with waveguide filters, couplers, etc. (usually the geometry is designed and simulated in a field solver first, and then imported in, but you can do it straight in the software if you want).

The easiest way is to design the coil as a part, but you can use traces and arcs and stuff like normal in that.

That works well if your coil component is small and is just acting as a microwave RF component or something, but in my case I had a pretty complicated coil design (although simple conceptually) that spanned the entire PCB and interwove with other coils and wasn't arranged in a simple rectilinear manner. My original plan was to design the whole thing in Solidworks, which I did (and it was pretty easy to do), but there was simply no easy way to convert that into an actual PCB for manufacture (there is a Circuitworks module, but it's designed only for importing circuits to design around in Solidworks, not the other direction). Sitting there and manually making arcs and such in the PCB design software was just a non-starter. There are no parametric modeling features to speak of, and it's actually way easier to do what I did.

I think I used OpenSCAD to export to SVG.

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