Personally, I think it looks bad when a complaint is raised against a moderator and that moderator doesn't comment on it. But, it can be grating as a moderator to defend your actions sometimes. There is also the problem of a complaint not being resolved properly coming back to haunt you in the future, as it can paint how users who read the interaction in the future view your capabilities as a moderator. Assuming your interaction is available for others to see. Though even if it's not public information, I would say that it's still important to consider how your fellow moderators view you.
My solution, as the moderator with the complaint against me, is to leave a short comment. Simply state why you took action, that you believe you acted within the community guidelines (assuming you have), and that you've asked another moderator to review your actions to verify that.
A little side-note: It's usually best not to ask a specific moderator to do this, or at least don't mention that you've asked a specific moderator, as it gives more credibility to you if it's a random selection. If users think you hand-picked someone to review your work, they might think that you selected someone specifically because you think they'd agree with you. Although, you can work this to your advantage, where if you can find a moderator that you know disagrees with you at times, but will agree with you this time, it could help to strengthen your argument that you did nothing wrong.
Now, the moderator that has reviewed your actions should give the user their unbiased opinion. If they did find that your actions needed to be reversed, you should politely apologize and thank the moderator for helping you. If they agree with your actions, they should state so, and why they agree. Sometimes it's helpful as the reviewing moderator to mention that you would have done the same if you were in their place.
The purpose of this is to show that your actions are not unique to you as an individual, rather that they're commonly shared across the moderation team and therefore the community that elected them.
Finally, you'll want to make sure that the user is understanding of the actions, and where the moderation team stands. They don't necessarily have to be happy with the decision, but if they still do not grasp the reason why the actions took place, or why those rules are in place, it can bring back similar problems in the future.
This can be as simple as directing the user to a page on the website that defines what the site is about and what actions are expected of users, or your having a conversation with the user and explaining it personally to them.
And above all else, keep it civil, be professional, and be respectful.