I recall only one whalewatching company called Whale Watch Kaikoura. They can be reached at 64-3-319-6767, or if you are in New Zealand, at 0800-655-121. It is usually necessary to book three or four days in advance, but most importantly, it is crucial that you are a bit flexible in your plans. While the tours start very early in the morning, at 5:30 am and runs through about 3pm in the summer (check this before you go), with almost hourly departure, bad weather can result in tours after tours being canceled. So if this is a must for you, allow for some leeway in your plans.
I of course did not follow my own advice, but I did not know any better when I got to Kaikoura. Fortunately, we got real lucky. When we approached the counter to pick up our 1:30pm tour, my two traveling companions and I were informed that all of the morning trips were canceled, and while the 12:30 pm did take off, it was very choppy. As we were supposed to be in Wellington by that night, we were really trusting it to lady luck. While the tour did go on--we were extremely lucky--I would not recommend this approach for anyone
whom whalewatching is a must see.