Answer: Trumpet Vine (Campsis radicans) is usually propagated by cuttings, either tip cuttings (taken in June or July) or root cuttings. When started from seed, the seeds are planted in the fall because they require a cold period in order to germinate, so I think you have several options.
First, allow the seeds to ripen in the pod naturally for as long as possible, then plant them outdoors this fall at your new house in a carefully marked spot. However, and this is especially true if your vine was a named selection, the seeds may not produce an exact match or as nice a plant as they one you have now. (This is due to natural variation is seedlings.)
In order to have the identical plant, you will need to propagate it by a cutting. (There are a number of entries in the Q&A database so you might check there for more instructions also.)
It is a bit late in the season to root a tip cutting, but you could try. Take about a six inch piece from the tip of a vigorous shoot, dip the cut end in rooting hormone, and stick it in a pot of moistened, clean soil mix or perlite or vermiculite. Firm the soil well, then place the pot in a plastic bag with the top slightly open to allow a bit of air circulation. Place the pot in a bright spot out of direct sun and cross your fingers. Keep the soil moist but not soggy, open the bag more to increase the air circulation if you see any fungal growth. Since it will be barely rooted, you will need to shelter the plant over the winter in a cool yet protected spot (a cold frame would be perfect) and then plant it in the ground next spring.
Finally, you might try root cuttings. With a sharp flat spade, dig straight down next to a shoot and try to separate it from the main plant along with some attached roots. (Fill in the resulting hole next to the parent vine.) Trim back the top vine on your root cutting to about 18". Transplant immediately to its new location; water it in well and mulch. Keep the surrounding soil moist but not soggy until the ground freezes. (If traveling, keep the root wrapped in moistened newspaper in a plastic bag, do not allow it to either bake in hot sun or freeze.) Next spring, it should leaf out and grow. This sounds the most radical of the three but would probably have the best chance of success.
All in all, it might be easier to buy a new plant, but I do know the feeling of wanting to take a favorite along! Perhaps the new residents would allow you to come back and take some tip cuttings next summer? Good luck with your trumpet vine!
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