It depends on what you mean by humility.
The definition I'm using here is basically "respect for the abilities of others and willingness to accept that just because you aren't good at something doesn't mean it's worthless". This distinguishes from related qualities such as obedience, and allows them to still recognise their own strengths.
As you've identified, this is normally more of an issue among children who are used to excelling in the fields that are valued within their social groups or authority structures, which can lead them to dismiss those values. (For example, intellectuals who dismiss the tremendous amount of work it takes to become genuinely good at sport, and vice versa).
For example, school is designed to emphasise and test two particular measurable skill sets (intellectual and sporting), and in some cases, streams those who excel in those fields, so that they focus on their strong area, and avoid their weaker areas.
One thing that can help is to get your kids more involved in co-operative team activities that require many different skill sets, such as volunteering or drama. This allows them to demonstrate their own competencies, but also exposes them to people who have focused on something completely different, that is nevertheless valuable.