Combine Greek yogurt, cilantro, parsley, Parmesan cheese, and Romano cheese in a food processor.
Blend until you get a smooth mixture.
Peel the garlic cloves and chop them into small pieces.
Add the garlic to the processor.
Pulse a few times to combine.
Squeeze the juice from half a lime into the mixture.
Add fresh dill, salt, and pepper.
Process until well combined.
Taste the pesto and adjust salt and pepper to your preference.
You can also add more lime juice if desired.
Transfer the mixture to a serving bowl.
Chill in the refrigerator for at least 30 minutes to allow flavors to meld.