How do I attach a Classic Car Badge without drilling holes?
 

How do I attach a Classic Car Badge without drilling holes?
Older classic cars have nice chrome bars to attach things to.

How would I attach a Classic Car Badge to an XJS or XK8?
I am not willing to drill holes into anything. No duct tape either.

Here are two examples:

JDC Shop - Car Bar Badge

JDC Shop - Car Grille Badge

put double sided tape on the back and cut out anywhere that you dont want it and apply it to the car. If you do it right youll never know its tape

yep. 3M double sided automotive tape. Comes in different sizes, available on amazon or Autozone, etc. Use an exacto knife to cut it just smaller than the badge. Wipe car spot with alcohol. Mark location with masking tape to guide the installation because once you stick it on, it's not coming off easily.