They should test for both EBV and CMV (cytomegalovirus) in both you and your recipient. As Karol said, both of these are very common viruses that most individuals have as children, and in many cases not realize it. They are both like the chicken pox virus in that you never get rid of it - it just goes into hiding. They test not with an eye to dismiss you as a donor, but as protection for your recipient. Because of the immunosuppressants, if the recipient has not had either of the viruses, the potential exists for them sero-convert form your kidney if you have tested positive. Both viruses can be more of a problem to them as an adult and immunosuppressed individual. The transplant team needs to be aware if your recipient is negative so they can look for signs and properly control the virus after transplant. My husband and I were both EBV positive, but I was CMV positive and he was CMV negative. For 9 months after transplant he took an anti viral (Valcyte) to keep the CMV at bay. They knew he would get CMV -that they could not control. So what they did control was the timing and get him farther out from transplant- once the anti viral was stopped, he started exhibiting CMV symptoms and they then began to work with his medication to control control the virus and put it "back in hiding".
Hope this eases your mind, Eva.