S.,
Congrats for doing such a breastfeeding your little one and giving them the very best thing you could offer!
Is there a reason that you want to wean right now and is that decision set in stone? If given the option and/or asked the question, most toddlers at 13 months would say that they still want to nurse, as you have experienced with your child. It's natural and serves not only as excellent nutrition, antibody benefit, emotional support and security. If you are willing to continue it will continue to provide so much for baby, as well as you health-wise, but if you are set on weaning I would recommend reducing 1 nursin session per month (starting with the one he will care the least about and miss the least)....and gradually continue taking away one each month until you are down to a number of nursing sessions per day that you are ok with, or are completely weaned. This will not be an easy process since he isn't ready, but it can be done. Keep in mind that although YOU are ready, he sees the nursings as far more than just a drink, so a sippy or other cup is not likely to serve as a true replacement, since he is only 13 months old and is looking for the closeness, comfort, love and security that he associates with being nursed by you. You may have to be creative in changing daily routines so nursing isn't an expected next event...such as if you always have bath, then rock in the rocker/nurse before bed...you may have to do bath in the morning and Daddy puts him to bed, etc.... Bedtime, naptime, waking in the am are likely the hardest/last to wean since they associate those with so much love, comfort while sleepy.
You may want to join the Yahoo egroups that are specifically for those moms nursing beyond 1 year old.... they offer specific advice on this very topic that you will gain alot from. There is one called Extended_Nursing and another called breastfeeding after one or something like that.
Go slow, be understanding and loving to his new confusion/stress that weaning before he is ready may bring...and hang in there! Best wishes....