The phrase "give a going over" implies an inspection or evaluation with a critical eye. Antonyms for this phrase could lean towards the positive or the gentle side of evaluation. For example, antonyms could include "praise," "compliment," "encourage," "support," or "commend." These words all suggest positive feedback rather than critical analysis. On the other hand, antonyms could also lean towards the more neutral or objective side of evaluation. Antonyms in this vein could include "ignore," "neglect," "overlook," "dismiss," or "shrug off." These words suggest a lack of scrutiny rather than a thorough examination.