The Eleventh Doctor

If the first triggered ability of suspend (the one that removes time counters) is countered, no time counter is removed. The ability will trigger again at the beginning of the card's owner's next upkeep.

If an effect refers to a "suspended card," that means a card that (1) has suspend, (2) is in exile, and (3) has one or more time counters on it.

You can exile a card in your hand using suspend any time you could cast that card. Consider its card type, any effects that modify when you could cast it (such as flash) and any other effects that stop you from casting it (such as from Meddling Mage's ability) to determine if and when you can do this. Whether you could actually complete all steps in casting the card is irrelevant. For example, you can exile a card with suspend that has no mana cost or that requires a target even if no legal targets are available at that time.