Using calculator "Delay" function.
You should point input threshold, output threshold and input and output edge type (rising or falling) and edge number. Then you can plot this expression or print in ascii file.
Another question, how can I make multiple measurements and save the results into one ascii file using Analog Artist? Or can I write a script to do this routine job automatically?
What do you mean multiple measurement? Do you want to run parametric analysis with Cload as parameter (for example) and then print delay for different Cload? If so you should go the same way. After that you can click "Plot" or "Erplot" (erase and plot) and you will get waveform that will show how is delay changed with Cload. X axis will be automatically changed to Cload. If you want to print this waveform in ascii file click printvs and fill in "From" "To" and "By" and click "Apply".