Relocate the plants to a wind-sheltered location on the balcony. If possible, push containers up against the building. Heat escapes from the structure, especially through the windows, and can raise the temperatures slightly in the air to help the plants escape cold damage.
Insert 1/2-inch diameter wooden dowels into the soil in the plant containers to create the support structure for a heat-trapping tent of fabric. The length of the dowels depends on the height of the plant in the container. Insert the dowel deep enough so that it's sturdy, but the top of the dowel is 6 inches above the tallest reach of the plant. In smaller containers, one dowel in the center may be adequate; insert two or three on the edges of large containers.
Place a string of miniature incandescent outdoor Christmas lights atop the soil in the container all around the plant you wish to save. A small container may only need a 35-light set, whereas a larger pot would benefit from a 100-light set. Run a weather-safe extension cord to the lights to illuminate them and give off a small amount of heat. If the overnight temperatures aren't to drop below 28 degrees Fahrenheit, using Christmas lights for heat isn't necessary. However, some plants are more sensitive to cold; one plant may be fine at 30 F, while another blackens and turns to mush.
Place an old fabric bed sheet over the dowels to create the tent over the container. A lightweight blanket also works as long as the support dowels can hold the weight. Let the sheet hang down over the plant and the container. Tuck the fabric ends under the container or place any weighted item on it to prevent any wind from displacing the sheet. You don't want a gust to blow the cold up onto the plant under the tent, nor do you want the fabric to displace and expose the plant to cold air.
Unplug the Christmas lights once outside air temperatures again warm above 32 F. The fabric tent traps the warmth for a couple more hours. Remove the sheet by mid-morning to allow fresh air and light to reach the plant, allowing respiration and photosynthesis.