To determine the minimum number of children required before you can guarantee that at least two of them share the same birth month, we can use the "pigeonhole principle."
There are 12 months in a year. If we want to avoid having two children with the same birth month, each child must be assigned to a different month. Therefore, if we have 12 children, it's possible for each of them to be born in a different month.
However, upon adding one more child (a total of 13 children), at least one month must then contain at least two children, because there are only 12 months available.
Thus, the minimum number of children required to ensure that at least two of them share the same birth month is:
\[ \boxed{13} \]