Do you want your kids to be "tough", or do you want them to be "sensitive"? Do you want them crying when they fall down, or do you want them to get up walk it off? Do want them getting their feelings hurt because someone doesn't like them, or do you want them to shrug it off and say, "Oh well, it's their loss."
It all comes down to balance - It's not good to be oversensitive, and it's not good to be insensitive. We all want our kids to be emotionally strong, but at the same time we want them to be compassionate. - You don't want a "crybaby" and you don't want a "bully." Ideally the child should have a healthy balance of being tough when tough is needed, and being soft when soft is needed.
"So how can I help them build resilience?"
The most important thing is strong and healthy self-esteem. They have to still feel good about themselves even when they fail. People with emotional security accept failure better than people who are emotionally fragile.
Provide them with non-stop never-ending love.
Provide them with challenges and opportunities to independently overcome adversity.
Teach them how to find solutions to every problem. (If a problem can't be completely solved, there is still a way to improve the situation.)
Summary
The best way to strengthen resilience is to build a strong emotional foundation based on love. Once this is secured, let them experience solving problems independently. Whether the problem is tying their shoes, or being socially rejected, the strategy is the same. Show them that no matter how bad things get, that alternatives exist, and they have the power to find them.