Our eldest participated in MOEMS for three years through a private Math Club. His scores improved on the contests, he liked the experience, and he has done well on other math tests and contests.
He has not participated in the Continental Math League, but there is a series of inexpensive books, for example
Math Contests, Grades 4, 5 & 6, Vol. 5 Paperback (2006)
by Steven R. Conrad and Daniel Flegler
with questions from CML contests that he has tried. I think the questions are interesting and may order some more books for my younger children, who are in grades 2 and 3.