Presenting the child(ren) with a meaningful gift in a ritualized manner is a great way to include children since they have something tangible as both a memento of the occasion and a constant reminder of their cherished place in the family.
I have seen parents present their children with rings, necklaces/lockets, watches, favorite books, and even a compass. When presenting the compass, we explained the symbolism to the boys reassuring them that no matter where they found themselves in life, they would always be able to find their way back home and be accepted with open loving arms.
There is no standard ritual for such gift giving. This portion of the ceremony can be customized in many ways. If there is special symbolism associated with the choice of gift, it can be explained to the children and the guests. The ritual can be phrased using age-appropriate vocabulary depending upon the age range of the children. Older children sometimes like to say a few words to their new step-parent at this time. The parents can include or omit pledges to their children. I do discourage children being asked to make vows to their parents. That simply is not appropriate to ask of a minor in my opinion. The parents are the responsible parties and therefore any pledges should come from them.
The following is an example from an actual wedding I officiated earlier this year in which the children were between the ages of 10 and 18.
Family Pledges / Gift Presentation
Marriage is often viewed as the union of two persons, but in reality the relationship is much broader. It is always a joining of families. Today we recognize their children and their importance to this family.
(Children), you will have a share in this marriage, for your lives will be touched by the promises made by your mom and dad today. Your participation is necessary to develop the bonds of this new family. Today, you all join together to create a family of mutual help, respect and support. May you all help to create a home and a way of life in which all may become the best people you can be.
(Bride and Groom), as you give yourselves to one another in love and loyalty, will you also promise to always keep room in your new life together for your children? Will you commit yourselves to respect and honor them as both individuals and as members of this family? Will you pledge to cherish, encourage and nurture them for as long as they need you? ~ We will.
(Children), as a symbol of their love for you today, your parents would like to present each of you with a gift. Let this token always remind you of the love that has brought you all together this day and will continue to guide and nurture you in the years ahead.
-- (Bride and Groom) present the children with their gifts.
May your love for one another continue to grow in ever widening circles of shared concern and mutual care.