General antonyms:
* Ignore
* Disregard
* Mind one's own business
* Leave alone
* Refrain
More specific antonyms depending on context:
* Help (if meddle implies interfering negatively)
* Support (if meddle implies hindering)
* Encourage (if meddle implies discouraging)
* Respect (if meddle implies disrespect)
* Trust (if meddle implies distrust)
The best antonym will depend on the specific context in which "meddle" is used.