Ambulance bosses are investigating why it took four hours to respond to a call involving a woman who later died from a drugs overdose.
They are also looking into an incident involving someone who attempted to hang themselves at a magistrates' court. They later died.
They are two of 27 investigations being carried out into serious incidents across the East Midlands. The first, in February, involved a 61-year-old woman who was reported to have taken a drugs overdose, but an ambulance crew did not reach her for four hours.
An inquest into her death is to be held in the future.
The second incident, last December, involved a patient who tried to hang themselves at a magistrates' court.
In a report, Karen Glover, Emas' director of nursing and quality, said the crew which responded to the call had inserted a breathing tube – to help revive the patient – down the patient's oesophagus, instead of the wind pipe. The report states there were 53 serious incidents in which 13 people died between April 1 last year and the end of February this year.
In a statement, Emas said: "In the year to date, Emas crews have responded to more than 550,000 emergency calls.
"The number of serious incidents reported equates to 0.009 per cent, or a serious incident every 10,377 jobs."
He said staff are encouraged to report incidents "so we can learn from near-miss, as well as actual harm incidents, and action can be taken to avoid any future harm".
The spokesman said: "We proactively publish this type of detail in order to be a transparent organisation which can learn from mistakes and accidents.
"Many of the incidents in question relate to a delayed response to 999 calls.
"Our Being the Best plans will help improve the speed at which we respond."
Dr Mike Pepperman is a former member of the health watchdog, the Leicester Local Involvement Network, which has been replaced by Health Watch.
He said: "Any incident is unfortunate and no-one wants them. However, the most important thing is that staff report any incident and it is investigated.
"It is also important that each is looked at as critically as it can be."
Zuffar Haq, of the Leicester Mercury Patients' Panel, said: "I am very worried about some of these incidents and poor performance."
He encouraged people to speak up if they experienced poor performance.
He said: "They should complain if they find that they feel the service isn't getting to them on time."
