Only sent campaigns can be selected. Draft campaigns won't appear in the dropdown until they are sent to at least one recipient. In order to select a campaign from the dropdown, it must be in Sent status in Campaign Monitor first.
If the error message
authorization failed: api.createsend.com returned (401) Unauthorized and said "Must supply a valid HTTP Basic Authorization header" is showing when trying to connect a Campaign Monitor account, it's possible the wrong key may be getting used.
In Campaign Monitor's "Manage API keys" settings, note that the API Key needed requires clicking "Show API key" first. Using the "Client ID" leads to this error.