Well… It depends what form of EMP you’re talking about. An electromagnetic pulse can take many forms and be delivered at different intensities, it’s kind of a blanket term. Let’s look at it from the electrical perspective and the magnetic perspective.
Lightning strike: The insulation provided by the glass or biopolymer is too great relative to your flesh. The voltage from the lighting would pass around your implant (assuming it wasn’t a direct strike on your hand). See this post
Solar flare/exploding transformer/EMP weapon: To affect the implants with a high intensity magnetic field, some of the field would have to be oscillating very near to the resonant frequency (13.56MHz or 125kHz) of the LC tank circuit. Any other part of the magnetic field would be attenuated out of the signal and not delivered to the implant. A broad spectrum EMP (like those generated by the sun) might have a high enough amplitude in the specific frequency range of interest to fry an implant. At that point, it would come down to what kind of ESD protection there was on the antenna pins of the IC, which is different for every chip. Many chips provide >8kV protection on input pins, so I think you’re probably good given the specificity of the frequency required. There’s not going to be a tuned 13.56MHz EMP bomb going off any time soon (ever?).
I think the moral is that your body and the encapsulation provide a huge amount of protection for your implants, and if anything were to compromise that you’ve got some bigger problems.