This is not going to be related to Sidekiq (well, not directly, anyway). This relates to whatever SMTP server you are using and the server's rate limiting. If you have multiple instances of Sidekiq firing off emails near simultaneously, this error might get thrown if you have a relatively low rate limit.
For instance, if you are using Mailtrap as a SMTP server in a development or staging environment, a free account is limited to 2 emails per second. Pretty easy to run into this error.
If you can't avoid running into this issue for your purposes, you can try a few different strategies by using the keyword argument 'wait' for ActionMailer's deliver_later method, e.g.:
users_i_need_to_email.each_with_index do |user, index|
t = 5 * index
UserMailer.send_important_stuff(user)
.deliver_later(wait: t.seconds)
end
In the event your :deliver_later calls are operating in different processes or flows, you can get away with randomizing the delivery time (say, some random time up to 5 minutes).
Obviously, neither solution above is full proof, so you are best off using a SMTP server that is adequate for your purposes.