Herpetologists are a pervy bunch (pdf link).
Once a male turtle was captured, we attempted to induce an erection by applying an 18 cm, variable-speed, silver bullet vibrator to its shell and tail. We vibrated turtles for 10 min or until an erection was achieved, and we recorded the amount of time that it took to induce an erection. Trials were scored as “unsuccessful” if an erection had not been induced by the end of the 10-minute trial period. Our preliminary trials indicated that turtles needed to be fairly relaxed and willing to extend their limbs and tails before the method would be effective.
They seem to have been fairly creative in trying to figure out how to give turtles an erection.
…the methods that have been proposed so far appear to be species-specific and have only been applied to common snapping turtles (Chelydra serpentina), whose penis can be everted by gently bouncing a turtle up and down (De Solla et al., 2001; Dustman, 2013), and Cotinga River toadhead turtles (Phrynops tuberosus), whose penis can be everted by immobilizing the neck and limbs (Rodrigues et al., 2014).
There’s also a detailed discussion of technique.
In general, turtles appeared to respond best when only the tip of the vibrator was touching them and when the vibrator had fresh batteries and was set on the fastest setting. Also, they seemed to respond best when the tip was held firmly against them (rather than allowing it to bounce), but not be pressed hard against them. Both allowing it to bounce and pressing it too hard generally resulted in turtles holding their limbs and tail tightly against the body, rather than relaxing. Additionally, it was often useful to move the vibrator around in small, slow, steady circles. As a general rule, we tried to hold the vibrator against the tail whenever possible (including following the tail if the turtle is waving it from side to side), but if this caused the turtle to retract its tail, then we moved the vibrator to a different position until the tail was extended again. Finally, sometimes males only protracted their penises briefly and quickly retracted them, rather than maintaining an erection. Therefore, it was necessary to watch the cloaca closely.