The site that you referenceBitaddress.org itself allows you to create Testnet addresses: https://www.bitaddress.org/?testnet=true(hat tip to Nick ODell). The generator for testnet addresses can be found by appending (Hat tip to Nick ODell)?testnet=true
to the URL. The site now appears to put the release version in the URL, so the link to generate a testnet address on bitaddress.org is https://www.bitaddress.org/bitaddress.org-v3.3.0-SHA256-dec17c07685e1870960903d8f58090475b25af946fe95a734f88408cef4aa194.html?testnet=true
On the other handNote that using an online website may be a convenient approach to generate a testnet address quickly. Do not use online websites to generate mainnet addresses, especially not if you intend to transact significant sums.
Alternatively, you could simply use a wallet that supports testnet, see e.g. Running Bitcoin Core in testnet mode.