This is a great question, I'm sorry to see no answers. The first step is to figure out which one it is: a tantrum is an intentional protest of a situation that the child feels unfair but a meltdown is something they have no control over. In some cases, look for the triggers. Sometimes we cause them (withholding something we want) and sometimes they're environmental (things we might not even notice, like a loud motorcycle, a barking down, a reflection flashing in their eyes as they try to play). In both cases, a calm soothing reassurance is your best route. If it's a tantrum, it will show them that their behavior isn't having the effect they want. If it's a meltdown, it will give them something to focus on and try to emulate. Be there for them, love them, don't get upset or anxious. If you're out in public, speak to them but a little louder so everyone else can hear as well - let those around you know that you've got it in hand and that they should butt out and mind their own business.

This is an overly simple answer, I would also recommend Googling "meltdown vs tantrum"

Thank you for being there for your grandson and being so understanding and caring and for your desire to help them even more!