Grow honeydew on a full-sun site in soil improved with 4 to 6 inches of well-rotted manure or garden compost. Honeydew grows best in slightly alkaline, sandy, well-drained soil. Space plants 12 inches apart in rows 4 to 6 feet apart.
Cover the soil around honeydew in black landscape fabric to help warm it and control weeds. Place a loose layer of horticultural fleece over the plant to provide warmth and protection from insects. Hold it in place with stones, drawing the fabric beneath them to create a firm edge against the ground.
Water honeydew in the morning to allow water on foliage to evaporate during the heat of the day, or water only at the base of the plant to avoid getting water on its leaves. Wet leaves on honeydew are a breeding site for fungal diseases. Water regularly so that the soil is constantly moist, and then reduce watering once the melons stop growing larger. Water only when the top 1 inch of soil is dry.
Feed honeydew with an 18-18-21 fertilizer for vegetables, mixed at a rate of 1 tablespoon per gallon of water, or according to the manufacturer's instructions. Apply every two weeks.
Check honeydew leaves weekly for signs of fungal disease such as powdery and downy mildew, which appear as white, yellow or brown patches. Spray with a ready-to-use fungicide containing copper octanoate, covering all parts of the part except the fruit. Spray every 7 to 10 days as long as symptoms appear, or according to the manufacturer's instructions. Honeydew growing in Tulsa and other areas of eastern Oklahoma are more prone to foliage diseases, such as downy mildew, due to high humidity.
Examine shoot tips and the undersides of leaves weekly for clusters of insects or eggs. Other signs of infestation include wilting shoots and holes in the leaves and stems. Spray all plant parts with a ready-to-use insecticidal soap spray at the first sign of attack, avoiding midday heat. Repeat every week as long as needed.
Remove horticultural fleece from honeydew when it begins to flower to allow bees to pollinate the blooms. Place developing fruit on landscape fabric, mulch or other substance to prevent contact with wet soil, which causes rotting.
Harvest honeydew melons when their skin turns cream colored and their ends give slightly when pushed. Tendrils near fruit may also turn brown and shrivel when the fruit is ripe. Leave 1 inch of stem attached to delay rotting in storage.