Corneal and lid margin sensitivity is tested with an aesthesiometer.
There are many types of aesthesiometers. The most common is the Cochet-Bonnet. It consists of a nylon monofilament of constant diameter which, depending upon its length, can exert more or less pressure. The length at which the subject responds to represents the corneal touch threshold. Others are non-contact, and use a pulse of pressurized air, or gas, to stimulate the cornea.
References
Cochet-Bonnet aesthesiometer
The American Heritage® Medical Dictionary.
2007. Retrieved October 2, 2015 from http://medical-dictionary.thefreedictionary.com/Cochet-Bonnet+aesthesiometer