Your question is open ended with not much information to go on. What type of trees? How tall of trees? This would help answer how much shade the clematis would be in and therefore the varieties of clematis that might do well with less light. For shrubs, the integrifolias do well sprawling through the smaller shrubs since the shrubs would be the support for the plants. Any of the vining clematis types would do well in larger shrubs. The only caveat is to determine when the shrubs will need trimming so you don't end up cutting the flower buds off the clematis before they bloom.

I have all kinds of trees!

Sycamore
Dogwood
Apple
Tulip Poplar
Catalpa
Maples
Walnut
Bradford Pear
Several that I haven't ID'ed yet. (new ownership of property)

Thanks

Maples (especially Sugar and Norway) will kill anything within their drip lines: they have very aggressive shallow root systems. Walnuts are poisonous for other plants, do not plant anything around. Sycamores grow huge, so "interplanting" with them is not the right term IMO. I am not sure about other trees you have. Shade is a minor problem compared to competition with tree roots. Trees with tap roots are more suitable for planting other plants around them.

I am afraid that most of the trees you mention will ultimately, if they aren't already, get way too tall with trunks that wouldn't allow the clematis much to grab onto to allow them to climb them. Dogwoods and apple trees might be the exception to the list. Too bad it is uncertain whether montana clematis would bloom in your area since they can get huge and once they got into the canopy, they could easily survive in the larger trees. I personally have type III clematis growing in a japanese maple, japanese styrax tree, a fosterii holly bush, variegated privet bush, a Otto Luyken laurel bush, and some others that I have probably thought of.

Alina, not too sure about the tap root thing. Most trees and shrubs have fibrous root systems and clematis can grow around them with no issues provided they are given enough water and nutrients. If you google trees and taproots, you will find several articles disputing the idea that trees have taproots. Here are a few quotes I found.

"Most trees do not have tap roots. In sandy, well-drained soils some trees such as oaks and pines develop deep roots directly beneath the trunk. These are commonly called tap roots. Many trees never develop tap roots. When the water table is close to the soil surface or when the soil is compacted, tap roots do not develop. Tap roots generally do not form on trees planted in our urban landscapes."

"Most trees begin life with a taproot, but after one to a few years the main root system changes to a wide-spreading fibrous root system with mainly horizontal growing surface roots and only a few vertical, deep anchoring roots. A typical mature tree 30Â50 m tall has a root system that extends horizontally in all directions as far as the tree is tall or more, but well over 95% of the roots are in the top 50 cm depth of soil."

"MYTH #8: The root system of a tree is a mirror image of the top. Many people envision a large, branching taproot growing deep into the soil. Actually, taproots are very uncommon in mature trees. If taproots do develop, they usually will be forced into horizontal growth when they encounter hard subsoils beneath the surface. The entire root systems of most trees can be found within three feet of soil. The spread of the root system however, can be very extensive, often extending 2-3 times the spread of the crown."

I'm not sure I'd make these statements quite that absolute :-)) - there are a good many plants that will grow under the canopy of maples (those that are adapted to dry shade) and walnut toxicity is limited to certain plants only. Clematis tend to be one that is quite tolerant of juglone.

However, the underlying concept is sound - these are trees that grow to very large sizes and large trees develop large, aggressive root systems; a difficult situation to get a clematis vine to establish and thrive. There is also the issue of excessive shade and/or how high these trees branch - too far off the ground and you will need to provide some other form of support. Seems kind of counterproductive :-)

The dogwood and apple are most suitable of the ones you list - they tend to be small to medium sized trees and can nicely support a clematis, provided you find one that grows large enough to provide a presence. I have a C. orientalis growing through my apple, but a tangutica or a montana would work also, if sufficiently hardy for you. I'd hesitate to suggest SAC, as that clematis is SO aggressive, it could devour a smaller tree and affect its health.

And Miguel, you are quite correct about tree root systems. Generally tap roots are a juvenile issue that trees outgrow with maturity OR they are a response to very arid conditions. The majority of the root systems of virtually all temperate climate trees are contained in the top 12-16 inches of the soil. And contrary to common belief, they exceed far beyond the canopy dripline, often 2-3 times (or more) the height of the tree.

GG, glad you chimed in here. I wondered about the walnut and juglone since I had heard others say that they grew clematis near one and they did fine. Didn't know if it was one of those things where it works for someone and not someone else either--not that I have to worry since there are no walnut trees in my garden.

Good to know that what I thought I learned in my one botany class was correct GG. I had to go back and goggle it to make sure. The next stop was the botany book that I used in college but then again so many things change over the years perhaps my botany book from 1981 would say something else! LOL

The majority of the root systems of virtually all temperate climate trees are contained in the top 12-16 inches of the soil.

I wish my trees knew this GG :o) I am trying to plant my Clematis and other perennials outside the drip line of the Maples and Sycamore (you are absolutely right about roots exceeding far beyond the canopy line). These tree roots seems to go to the center of the Earth... ;-)
Norway Maple on our backyard kept killing everything including weeds, no matter how well the plants were watered and fed. We removed it finally (it had its trunk split, so it became dangerous). Now I will try to plant Epimediums (which are supposed to be dry shade tolerant) under the Amur Maple. As far as I know, Amur Maple (as well as Japanese Maples) are not that aggressive. Wish me luck...
I will also plant a couple of Montanas not far from this Maple (again, outside the canopy line). I hope they will survive my zone 6-7 winter.

I also almost gave up on idea of planting Clematis in the vicinity of the Red Maple on my front yard. These fibrous roots fills any freshly dug hole in no time. Maybe, I will try a cardboard casing for helping Clematis to establish. I always wanted a Clematis next to my mailbox...

As for tap roots, it might not be the exact term, but Oak roots are really different (in terms of digging around them).
As always, I really appreciate your comments GG and Miguel! You are my experts :o)

Thank you for your advice, I do have a Sweet Autumn Clematis that I will be transplanting from my current home to our newly purchased property.

As far as things that would possibly work I also currently have: Japanese Maple 'Atropurpea ?sp? , Magnolia 'Jane", Lilac 'Little Kim' and two unknown varieties, 2 unknown Hydrangea, unknown Holly and several others that could possibly work.

This is slightly OT but can/should Clematis be interplanted with Wisteria?

Off all the new plants you mention Bonnie, I think all but the Magnolia 'Jane' would work. I excluded the magnolia only because I am not familiar with that cultivar. Perhaps someone else is and can offer advice.

The thing with any tree or shrub to consider is the stage of maturity that the plant is when you plant the clematis with it and how large the tree or shrub is going to be in terms of its spread outwards when it is mature. If you plant a clematis near a shrub when it is still immature and the plant grows to engulf it with its branches when it is mature, I would think it would be much more difficult to provide it with enough water and nutrients and the shrub may eventually smother it out. Just a thought.

I personally would be hesistant to plant a clematis with a wisteria due to my experience with growing wisterias. They tend to be very aggressive and would compete so much with the plant for water and nutrients that I can't imagine a clematis being happy coplanted with it. Perhaps someone else has tried this and can offer a contrasting opinion.