No, there's no need to worry about mistaken double payments. Contactless technology is set up to make sure a second tap isn't registered, and you're only charged for the transaction once.
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You can't pay accidentally—your contactless card or payment-enabled mobile/wearable device must be within 2 inches of the terminal for the transaction to take place. And you won't be billed twice, even if you accidentally tap twice.
Because no signature or PIN verification is typically required, contactless purchases are often limited to a maximum amount per transaction, known as a Cardholder Verification Limit (CVM limit). Limits vary between banks.
If your contactless payments are repeatedly denied even after a Chip & PIN input, however, there's either a problem with your card or a problem with the store. Perhaps a malfunction of sorts, or it has expired, or there's an issue with your account.