Here are the common causes for shudder:
Clutch disc contaminated A contaminated clutch disc can cause the clutch to grab, shudder, or even slip. Check for oil and coolant leaks around the back of the engine. Look for signs of oil or coolant coming out of the bottom of the clutch housing. Replace clutch disc if there are signs of contamination.
Driver induced shudder. Sometimes the way a car is driven can cause the clutch to be grabby or induce the shudder. There are basically two different types of drivers with regards to clutch operation. Those who feather the clutch and those who jab the clutch. Those who jab the clutch get on and off the clutch pedal very quickly when changing gears. Over time, this will tend the make the clutch grabby. Someone who feathers the clutch engages and disengages the clutch slowly. So, if you're one who normally feathers the clutch and you get in a car that's normally driven by someone who jabs the clutch, you'll likely notice a shudder when you engage the clutch. The advantage to gettting on and off the clutch quickly is that it normally extends the life of the clutch by reducing the amount of wear.
Warped pressure plate or flywheel. There's really no way to check for this without disassembling the clutch and inspecting the pressure plate and flywheel.
Worn splines on clutch disc. There's really no way to check for this without disassembling the clutch and inspecting the clutch disc.