Yup, it's a constant joke on the forum I'm afraid, being pee'd on

Many of us use a water-proof pee pad, you can use disposable puppy pads, old towels, anything suitable really.
Some are more polite than others. It doesn't occur to many piggies not to pee on their humans, some actually do notice. I had one, my first adopted piggy, and I think she thought that the pad I used was part of me, so she would always poke her bottom off the pad to wee away from it. It tended to land on the person sitting next to me (usually Mr Critter) or onto the settee, and then the pee would make it's way down-hill, down and to/under my legs where I was sitting. Nice.
Guinea pigs in the wild wouldn't have a permanent territory. They don't make nests and even when giving birth they don't have a nest as the babies are so well developed they follow the herd around from birth. They would move from one grazing place to another, so in terms of evolution there has been no reason for them to have to hold in their pee's or 'water' a particular area and keep other areas clean.
Sometimes a nervous piggy will pee. I have noticed when I take mine to the vets they will hold their pee in all the way, and then do one while being handled by the vet. My Penny is relaxed most of the time, but fusses about some things. She is a squirmer when it comes to nail and fur-clipping and it often results in a wee.
It can be a stress response, and some even do it deliberately when another piggy keeps bothering him/her, the botherer may end up with wee in the face!
Piggies CAN hold their pee for a short while, and some actually do realise that they are sitting on someone who doesn't want to be pee'd on (and some never realise). The ones who are needing to pee and don't wish you to get wet will often try to warn you by fidgeting and nibbling at your clothes. Take this as a sign to be placed on some litter or back in the cage for them to pee, and both of you will get used to the 'routine' of it.
For the ones that don't grasp that you don't like to be pee'd on, they may never understand, so it's best to place a towel or pee pad over your lap.
I recommend one to either side of you too (incase you have a polite one like my first who pee'd off the side).
Please don't be put off - they may get better with age, with learning to relax, and through you learning their pre-pee signals (for those that tell you), and have a pee-pad always!
