Ideal is if you can catch the kitty yourself. Just be careful and don’t get fooled by the apparent size or situation of a cat.
A kitten can become a vicious bundle of teeth and claws if it feels cornered. A grown up cat – even if injured – can be out right dangerous. So get some thick gloves (motorbike or gardening) on and keep a thick towel as well as a big box or basket with lid handy.
If you are not sure how to go about it, please get advice or help from a trapper or pest control organisation.
You have been successful and caught the cat yourself. Well done!
If you can foster the kitty yourself until you found a loving home that is great.