Perhaps Tango? How large are they? Can you add a photo of the inside of a flower? I was assuming that the inner part is red and white, but the outside is sometimes paler or darker than the inside, so I am not sure that this is a reasonable assumption. It is a Viticella hybrid, and perhaps a Viticella- Texensis hybrid.

Walenburg is another possibility.

It looks very similar to 'Odoriba'. Another possibility is a faded out (late bloom) 'Ladybird Johnson'. Older flowers can be quite dissimilar to a freshly opened one :-)

Thank you so much. The flowers are essentially gone now, but I was still able to find one and take a photo. The blossom is not in good shape but I compared it with all of your suggestions and think Tango or Walenburg look the most similar.

It has self seeded in my yard and I am giving a baby to a co-worker. I wanted to be able to give her an idea about the ID. Thanks again.

Since these are hybrids, any seedlings aren't the same plant. It may have attractive flowers that are similar to the parent but it may not. Sort of like your kids may look more or less like you. Vegetative propagation such as cuttings or rooting a branch is the only way to make one that will be completely the same.

Oh dear. Thanks for the information. I will have to see whethe my co-worker still wants to give the baby a try.

And I've been thinking about trying some cuttings, just haven't found the time.

Easier than cutting is to peg down a branch where a leaf attaches, cover it with soil and leave for a year or two. If you have rooting hormone, scrape the surface and dust it with rooting hormone before covering with soil.

Can I do this anytime of the year, like now? Or would it be better to do in the spring or fall?

I think now is just about perfect IIRC, and I would likely leave it until next fall (2018) before clipping it to separate it from the mother plant.

Look up clematis layering for specifics.