Take a little of chaka's and Ryans advice, and mix it with some of mine
Be very careful in your approach. I personally would consider letting them know there are some quite major security flaws in their site, and would they like to meet to discuss it.
If they want examples of the flaws don't give explicit details of them (or they will probably get their in-house team onto resolving it and bypass you), just give them very broad explanations (if at all). Tell them you are not there to make any deal, but only to let them know of their security flaws. Let them know you provide secure solutions and can help them out. If they want to talk business then tell them they can have a think about things and leave them your contact details to contact you if they require your services. let them know you can fit them in at any time (or specific time if you are fully booked), thank them, and walk out. Don't give them the hard sell.
3 days later send them a "thank you for the meeting" note, and maybe even a small personal gift (nice pen, gift basket etc). Do not hard sell them at all here. This is where you are building customer relations. Every time that person sees/uses the gift they will think of you and your security solutions. If male go for a nice pen or desktop gadget, female go for flowers or feminine decoration. This personal gift and handwritten note will get you further than any amount of talking. They realise you have given them a gift for nothing, so your advice must be sincere etc. If you do not get a contract this time you might have spent $10 on a future relationship with this company and it's network of clients/partners. That's called an investment.
If there is no reply, or meeting arranged, then contact them again within 3 days (6 days from first meeting). Let them know you were thinking of them, and were hoping they were closer to a solution. Wish them all the best and leave it at that.
If there is no contact from them, keep sending them a note, or email every week asking them how things are going etc. Be politely persistent, don't stop trying until they actually say "no".
Good luck.