I handle it just like you did Jags. Validate their fears so they know somebody is listening and reassure them the best you can. "Trust me" was something I used with Dad repeatedly. If I could get those two words through his fog he was always better because his long term memory told him he could trust me. Sometimes just holding them and being there is enough. My goal for Mom is contentment but the disease fights against me. It clouds her mind and puts her in a fog that is scary. Those with dementia need to let go of their emotions just like we do. We cry... they cry... and it is ok. It is an appropriate release of frustration and anxiety. So just hold her and let her let go. It is actually good for both of you. Then find a way to laugh.. even if it is chasing a red scooter around. Yep, that made me laugh! Dad wanted one so we took him to the local big box store and let him do a test drive. His inner race car drive came out and he was never allowed on one again!
Just glad the day ended in laughter and smiles. Take that part home with you and the fact that you were there to comfort your Mom in her moment of distress