Tom,

Thank you for your question. 

It is quite possible to grow tomatoes in containers. I have done this myself. 

Please read through the following CSU Factsheet regarding container gardens:

https://extension.colostate.edu/topic-areas/yard-garden/container-gardens-7-238

There is a side bar that has tips for vegetable gardening in containers. Be sure to use fresh soil or potting soil each year because pathogens and disease can stay in the soil, this is especially important if you have had any disease issue with your tomatoes in the past. 

We have had some very hot summers and your containers may need water more frequently. Be sure to check that the soil is moist 4-6 inches below the surface. Tomatoes need 6-8 hours of sun per day in order to thrive. If the temperatures during the day are above 90 degrees at 10am the plants may drop their blossoms  as a way to conserve moisture and energy. Your containers can increase the temperature of the plants roots and this may also cause blossom drop, so try to keep the plants adequately watered to help keep the soil temperature lower. Fertilize your plants every 2-4 weeks with a good fertilizer product for vegetables, following the directions on the product. You can fertilize tomatoes until the fruit begins to set and then you will cut off the fertilizer. Continued use of fertilizer will give you a lot of foliage growth but not good fruit set. 

You might want to try some determinate tomatoes such as 'Totem', 'Taxi' or 'Celebrity'. I have had good success with a variety called 'Gardener's Delight' which I have grown in a container. It is larger than a cherry tomato but not full-sized. You could try a cherry tomato such as 'Sweet 100' or 'Sun Gold' which do very well here in Colorado. Your local garden center/nursery may have varieties that are suited for containers as well. You will need to provide some staking or caging. Watch for pests and signs of disease. You can contact us for help with these issues if they occur.

Good luck with your tomatoes.