I have quite a few t-shirts that I love to wear, but the neckline is just too low for me. In the winter it's easy to layer with other shirts or tank tops. But in the hot summer, putting on yet another layer is out of question, as it defeats the purpose of a cool cotton t-shirt. I have tried sewing some modesty that clip to the bra straps, but I found that I had to fix it too often to be comfortable during daily wear. So, I just decided to sew some permanent modesty panels into my daily wear shirts and stop worrying about it.
For shirts I could find coordinating solid fabric, I used scraps of that and for those I couldn't, I simple used white t-shirt fabric (cut up t-shirts we received from the airline when we were stranded in a hotel last year because of a missed flight).
I am going to show you the process I used on one of the shirts. This method requires no measuring or making of any patterns. I first just eye-balled the width and length of the opening, then cut strips bigger than that. I hemmed the upper edge of the panels (on some I just used the bottom hemmed piece upside down, on others I bound the edge or used elastic lace).
Then I turned the shirt inside out and pulled it onto the ironing board. I placed the panel strip over the opening and first pinned, then basted it in place. I tried it on and fixed something if it pulled anywhere.
Then I used a matching thread on top and white on bottom and simply stitched the panel in place from the right side, stitching over existing stitches in binding or hem of the t-shirt.
If everything worked and it looked well, I cut off the extra fabric and voila - a shirt that is modest and comfortable. Here is the view from the inside:
And this is the view from the outside: