Being able to run J2ME on a phone or PDA is not the same as being able to run applets. Applets use J2SE, which is not compatible with J2ME. I don't think (not sure, though) that there are any hand-held devices that support J2SE.
Actually, I own on that does - the Sharp Zaurus SL6000. It's a nice device, now, alas, long since out of production.
I'd say obsolete, but it's really not that bad - 640x480 screen, Linux 2.4 kernel, Wi-Fi, Opera browser, touch screen, good battery life and rugged as a tank. I totalled a Handspring Visor dropping it on carpet from about 1 meter. I've done the same with the Zarus and the finish is still unscratched, much less the touchscreen.
The way it would run applets is the same way a desktop machine would. Use the Opera browser to visit the website and let it invoke the applet plug-in.
This is an ARM processor, and I don't know if there's up-to-date JVM's for later Java releases, but its Java support was a big selling point.
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