If my child doesn’t eat their meal, should I offer it to them again later?

The answer is No!

To which you might say …
Why not?!
If they haven’t eaten the meal I made, I don’t want them thinking they can just have something else instead.
It’s all about pressure! If you present them with their meal again, it shows your child how much you want them to eat it. This simply gives them something to react AGAINST. Remember the root cause of fussy eating is the power and attention a child gets for NOT eating something.
It also smacks of the old-school approach of “‘It’s that or nothing” or “‘If you don’t eat it now, you’ll have it for breakfast” – even if you don’t say anything like this! This creates negative, punitive feelings around food which is very detrimental.
So should I make them something else instead?

Absolutely not! If you let your child be in charge of the menu, they will go for their preferred foods every single time – and their diet will get narrower and narrower.

Then what should I do?
As your child gets down from the table, say to them very gently and casually – like you’re really not bothered either way – “I’ll just leave your dinner/tea on the table in case you want more later.” And leave it there for 30-45 minutes to give them a window of opportunity to revisit it – but no longer than that because you don’t want to encourage a culture of going backwards and forwards to the table willy-nilly all day long.
And if they do decide to revisit their meal, show no delight – and say nothing! In fact, act like you haven’t even noticed! If you praise them, you’re showing how much you want them to eat it again.
But what if they don’t revisit their meal?
You shouldn’t expect this technique to work immediately. Just keep doing it every day. But of course, meanwhile, you don’t want them to go to bed hungry. Whilst bedtimes snacks are best avoided if you can get away with it, it IS okay to give them one – so long as you do it in this very precise way described here that doesn’t exacerbate fussiness or encourage them not to eat their dinner/tea in the first place. 
To find out the whole “Getting the Little Blighters to Eat” approach to stop fussy eating in your child, visit stopfussyeating.uk