The local (Northwest) pronunciation of these is clem-AT-is and Pe-ON-ee.

However beig a long time gardener, I pronounce them the other way: CLEM-a-tis and PEE-on-ee.

When I get confused on pronounciations, I look it up and check several sources. I always go with the horticulturists.

Here they say wy-GEL-a and I say (or am trying hard to say) wy-JEE-la, as well.

Local gardeners here say wy-gee-lia. It does make one hesitant to say the name when touring others gardens. Perhaps that is why there are so many common names for plants. No one can mispronounce busy lizzy, mind your own business, wood sorrel, etc.