I have had multiple families choosing to have their children present regardless of age.  I have seen some children be present who probably should not have been but in my opinion, it greatly, if not mostly depends on how the parents handle it and on the parents' reaction to the euthanasia and their handling of the child.

I don't necessarily think that age is a factor.   Maturity is also relative and is not necessarily dependent on age.  

It is a very personal decision and I think that one of the best thing that a parent can do is to educate the child (in terms appropriate to age) as to what will happen.  I would also (of course depending on your spiritual beliefs) emphasize that your pet's BODY is dying and that your pet himself or herself will go on to his or her next adventure, whatever that might be and again, this depends on your personal spiritual beliefs.

After the child has been educated on what will take place, the other best thing that the parent can do is GIVE THE CHILD A CHOICE on whether or not the child WANTS to be present.  And make it clear that the child will have a choice on attending or continuing to attend throughout the procedure.  Make sure that the child knows that he or she can leave at any time and perhaps have someone who can be with a  young child if he or she decides that he wants to leave mid procedure, so that he does not find himself alone and scared and so that it does not interrupt your personal involvement in your pet's passing.

Very small children may not understand what is happening and if the child is not old enough to answer the question of whether or not he wants to be present, it is probably better not to have him or her be there.

If the child is old enough to have a conversation and understand what is happening with your pet, I would advise strongly against hiding the truth about what will happen.  Perhaps you have made the decision that it would be better for your child not to be present.  If this is the case, I would also advise you to let your child know that your pet will be euthanized beforehand as opposed to after the fact.  That way, the child will have a chance to say goodbye to his friend too.  If he has not had a chance to say goodbye, he may have regret in his heart about this for a very long time.

It is also very important that you choose a veterinarian who is comfortable with children being present and who does not disagree with the idea of children being around.

Another point to consider is to ensure that the adults around the child will be as calm as possible.  Doting a bunch of sympathy and "Ohhhhh  pooor baby...." is very harmful to a child's emotional state and can have lasting effects.  Of course, holding the child and being there for him or her and hugging him or her is perfectly fine.

Children usually cry hard and intensely, but frequently recover faster and better than we adults do...  So don't underestimate your children's strength and ability to recover and ability to handle this loss.

There is a wealth of information on my website that will help tremendously in educating yourself and your children regarding the procedure.   I also have a video clip of an in-home euthanasia that I am sure will be helpful.  It is done in a very respectful manner and very calming and reassuring.  Here is the direct link to the video on my website. On the rest of the website, you will find written information on how the procedure is done, you will also find information on the quality of life which will be helpful in preparing your children and in getting them to realize that your pet's life is not enjoyable anymore (or will not be at the time when you make the decision), you will find information on the aftercare so that everyone understand what will happen to the body afterwards.

Hopefully, all this will help you in deciding if your children should be present.