Both of these lovely orchids lost their flowers some months ago and I was wondering if there's something I can do to encourage them to flower again..?
Dendrobium - Polar Fire
Iwanagara - Apple Blossom (Blush 11)
The orchids are really happy, as both have new growth. Is the new growth taking all the energy away from producing flowers..? Will I have to wait for the new growth to produce the flowers, or will the older part of the orchid flower again..?
1) Iwanagara is now, courtesy of the taxonomists, Leonara, and as that is a "cattleya type" of orchid, they will never bloom from old growths, the flowers emanating from the crown of new growth when it matures. It helps if you realize that each growth is its own individual plant, and the old ones continue to support the new ones through photosynthesis and by being nutrient storage vessels.
2) Your dendrobium is not a registered hybrid, so we cannot look up its genealogy to help. As it looks like it bloomed from spikes growing from the tip of the cane, then it is likely that it is just like the leonara and will only bloom from new growths upon maturing, although sometimes they can grow new spikes a second or even third time.
The best way to encourage an orchid to bloom is to keep it as happy as possible. Proper water, fertilizer, light, temperature and humidity are vital to them. If you get good, vigorous growth which produces strong, plentiful root masses you'll get flowers. Strong plants have a lot of energy to use for blooming. Doing anything to push an orchid to bloom could harm it in the long run.
your new growth is not big enough to blossom. Try and wait. usually it should be bigger than the old cane. Looking at your photos uve shared i think they are in good shape and will grow bigger than the old. give them enough light (morning sun), your plant is in active growth therefore try to fertlize them (weakly). Good luck! Patience...