If you're gardening in an urban space, concerns about water runoff are completely valid. The short answer is: it depends. Many urban planter boxes do not automatically come with saucers or trays, but they're often available as separate accessories that are crucial for responsible urban gardening.
Most modern planter boxes feature drainage holes at the bottom to prevent root rot, but this creates the very runoff issue you're worried about. The good news is that numerous manufacturers offer matching saucers and trays specifically designed for their planter models. These catchment systems serve multiple purposes - they protect your balcony floor, deck, or patio from water damage, prevent staining, and can even create a reservoir of moisture that reduces your watering frequency.
For those living in apartments with limited outdoor space, using saucers becomes even more important to maintain good relationships with neighbors below you. When shopping for planter boxes, look for terms like "includes drainage tray," "comes with saucer," or "water catchment system." If your preferred planter doesn't include one, measure the base dimensions and purchase compatible trays separately. Alternatively, consider self-watering planters that have built-in reservoirs, which solve both drainage and frequent watering concerns in one elegant solution.
Remember that even with saucers, you'll need to monitor water levels to prevent overflow during heavy watering or rainfall. The small investment in proper trays will give you peace of mind while protecting your urban living space.