Give them a house key to get into the house after school. This is a huge step and can be a risky one if you are not looking forward to changing your locks or calling a professional locksmith when they lose their key. You may not be ready for them to be home alone yet so there are smaller steps you can take in the meantime.
Try dropping them off at the park near your home with a cell phone and have them play for an hour and walk right home while you run some errands. Not only will they need to pay attention to the time but responsibly walk home on their own depending on the distance of course.
The rules are different depending where you live but where we live you can leave your 10 year old at hone for a short amount of time on their own. An hour or so to run to get groceries and stuff like that nothing major. Letting them do this teaches them a great deal of responsibility for when you are ready to give them a key to the house.
Enrol them in a home safe course that teaches them different safety precautions and what to do in an emergency and how to act when they are home alone. We have plenty of places to enrol in these courses and you probably do to if you call around local recreation centres.
Take your time teaching them the proper way to behave when home alone and what to do in case of an emergency and they will be ready for their key to the house in no time at all.