Allow the tops of your seed cells to dry out before watering and keep air circulating around the seedlings - as the wind would do if your seedlings were outdoors - with an oscillating fan.
One of the biggest threats to indoor seedlings is damping off - a disease that causes them to suddenly flop over and die. The best thing you can do to prevent damping off is reduce the humidity and moisture around your seedlings. Allow the tops of your seed cells to dry out before watering and keep air circulating around the seedlings - as the wind would do if your seedlings were outdoors - with an oscillating fan. You can buy a mini fan and clamp it on the shelf holding your seedlings, or you can set one up you already have around the house, pointing towards your seedlings.