Water in the morning (watering at night promotes diseases). Agastache is fairly drought tolerant. Nevertheless, these plants can benefit from regular morning watering. Consider watering twice, a few minutes apart. This will help water soak in deeper.
Apply an all purpose granular fertilizer in midsummer according to label directions. This will help the agastache thrive and stave off insects.
Prune back stems in the spring, but avoid pruning in the fall or winter. According to the Washington State University Clark County Extension program, dead stems benefit agastache by providing some frost protection. In addition, they look nice when covered with snow.