I found this info at a website that has NoCDs available for download:
Moto Racer - CD-Checks
System Shock 2 - SafeDisc
Age of Empires 2 - SafeDisc (v1.50.020)
Turok: Dinosaur Hunter - CD-Checks
I'm not sure if I'm allowed to post a direct link to the website with the information, but you can find it with Google by searching for the name of the game and NoCD (for example - Moto Racer NoCD )
The following dates are from Mobygames
Moto Racer 1997
System Shock 2 1999
Age of Empires 2 1999
Turok 1997
The versions of SafeDisc used in such old games won't have much in common with the more invasive modern disc-based versions of SafeDisc that install filter drivers and who knows what else and leave that junk behind even after you uninstall the game.
"CD-Checks" could be a number of things, including checking the CD for the presence of Redbook audio files. There was a utility called "un-CDcheck" that could remove certain types of CD-Checks. I don't know if it would work for Moto Racer or Turok, but those games already have NoCDs available. The un-CDcheck utility might be more useful for games where there is no NoCD available.
For 1990's games it's probably possible to make a 1:1 copy that won't give that "put CD in drive" error -- provided your CD writer is good enough. Programs like CloneCD and Alcohol used to have an "approved" list for which CD writers worked best -- something to do with being able to read and write subchannel data or supporting "RAW".
Another strategy was to use a NoCD and modify the CD image by replacing the original game exe with the NoCD version of the exe (that has the disc check removed) before burning the CD image to CDR. You'd need software that allows modification of CD images for that.
Try Googling
Backup Protected Game CDs
for more tips.