Can an enquiry or proposal ceremony be held during Ramadan?

Yes; there is no Shariah prohibition on making an enquiry, proposing or getting engaged in Ramadan. In fact some families choose Ramadan because the atmosphere is calm and relatives gather easily. But plan carefully. Hold the ceremony after iftar or after tarawih so guests do not have to choose between worship and the event. A simple iftar meal can be a warm way to receive the party. Avoid discussions that run so long that people miss the congregational prayer. If the guests are coming from far away, take into account how tired they are from fasting and choose a weekend. See proposal (khitbah) guide.