Took the ex missus foamy (Laura) from Lydney to Bournemouth on the XJ, she was a natural considering she hadnt been on a bike before, i find its best to keep both feet on the ground and the front brake on whilst they are getting on or off and take everything nice and gentle, allow plenty of time for overtaking and braking (usually a good indication to the passenger that you are preparing to overtake is changing down a gear and doing a lifesaver check), other than that watch out for your pillion looking over your shoulder or moving around too much at slow speed or on corners, especially in traffic or when filtering as this will alter the bikes CofG and attitude, resulting in you altering your course to compensate.
most importantly of all, keep your bike up to scratch, check your tyre pressures and make sure they are in accordance with the owners handbook (most bikes have a section which describes the changes needed to carry a pillion, on the XJ it was +3psi in the rear tyre and up a position on the shock its one thing if i have an accident due to poor maintanence, but i never used to carry a pillion unless i knew for a fact that bike was in tip-top condition, if something happens to them you are accountable and will have to live with the guilt
also watch out for strong gusts of wind especially on a YBR, used to go across the seven bridge two-up and it was hard work when it was windy, sometimes leaning right over