Think about removing the outgrown pot from the plant rather than removing the plant from the pot. The idea is to slip the orchid free without damaging the fragile roots. Wiggle the plant and hold it firmly at the base while working the pot loose. Set the pot aside and remove as much old potting medium from the roots as possible. The cleaner the roots, the better access to new potting medium, water and air the orchids will have in their new container. Once the roots are clean enough to observe, cut withered, collapsed, mushy or darkened roots away with sterile scissors. Healthy roots are fat and firm with white tips.
Repot orchids in new containers that are barely 1 to 2 inches larger than the old ones. Swirl the roots gently into a curve in the new pot while holding the plant in place and carefully filling in with bark or other orchid medium. Position the roots by side slits if orchid pots are being used. Orchid pots are specially made to give the roots maximum air. Most orchids are epiphytes -- they grow in the crooks of trees or are otherwise suspended and draw their nourishment and moisture from the environment around them. When orchids are planted in a potting medium, an orchid pot with openings in the sides exposes the plant to more oxygen because the roots will grow right out the slits in the pot. Some nurseries suggest adding a layer of gravel in the bottom of the pot for better drainage.
If a transplanted orchid that was failing doesn't bounce back, it may need to be repotted a second time. The roots might have been so crowded in the original pot that they began to die. Trimming the damaged roots lets the plant focus energy on healthy roots and healing in its new pot. If the leaves wilt and start to wrinkle or shrivel, transplant the orchid one more time. This time revisit the plant to be sure all mushy or damaged roots were trimmed away. Cut the wrinkled leaves as well -- they can't be saved and the plant needs its energy to grow new healthy roots and leaves. Repot the trimmed plant in a smaller pot to encourage the medium to dry out more quickly. This lets the roots get more air. The remaining leaves should be joined by new healthy growth as the plant adjusts to its smaller container.
When it's time to transplant, increase the orchid collection. Cymbidiums propagate readily from division, so if a cymbidium is too large, create new plants when repotting. Cymbidiums love a really snug fit; transplant them only when they begin to crowd the edges of the pot. Their pseudo bulbs, swollen storage stems that typically have leaves and provide nutrients and water to the plant, are the parts that produce new plants. Trim large orchids with a number of pseudo bulbs as soon as they finish flowering. Cut the plant to preserve at least three pseudo bulbs with leaves for each new section. Plant the cuttings in pots that are just 2 or 3 inches wider than the orchids so they drain well, dry out and keep roots healthy. Be patient while waiting for cuttings to mature -- it can take two or three seasons before a transplanted pseudo bulb develops into a flowering plant.