For younger children, usually the simple task of holding the rings or bouquet is enough to accomplish a sense of participation.
The Bride and Groom light these candles, and then all together light the center Unity Candle.
Mentioning their name during the wedding assures that they are an important part of the occasion and have special status which guests and other family members attending do not. If children are coming into the marriage, it is appropriate to mention in the ceremony that not only is a marriage being formed, but also a family - and then name each child.
If a prayer is in the ceremony, each child's name will be stated in the prayer.
The bride and groom walk away and are crowded by "big people" - with the children left out of the immediate post ceremony celebration.
When children tend to feel most left out is immediately after the ceremony.