Not panicking and not overjoyous

Solution 1:

"This too shall pass" … is an adage indicating that all material conditions, positive or negative, are temporary.
The phrase seems to have originated in the writings of the medieval Persian Sufi poets, and is often attached to a fable of a great king who is humbled by the simple words. Some versions of the fable, beginning with that of Attar of Nishapur, add the detail that the phrase is inscribed on a ring, which has the ability to make the happy man sad and the sad man happy.

For me, Abraham Lincoln’s 1859 interpretation of the adage connects it well with the idea you describe of staying balanced and not letting anything get you too down with panic or too high with jubilation:

“… . "And this, too, shall pass away." How much it expresses! How chastening in the hour of pride! How consoling in the depths of affliction!”

(from Wikipedia)

“[Keeping] on an even keel” also comes close to capturing the notion of patient balance that you seek:

on an even keel

regular and well-balanced and not likely to change suddenly

(from Cambridge Dictionary)

Solution 2:

The idiomatic expression "stiff upper lip" is quite close to what you want.

Wikipedia:

One who has a stiff upper lip displays fortitude in the face of adversity, or exercises great self-restraint in the expression of emotion.

Solution 3:

There are many proverbs that say good times and bad times are connected, or that good and bad come one after the other.

Some old examples from Curiosities in Proverbs (D.E. Marvin, 1916):

Fortune and misfortune are neighbors. (German).
Fortune and misfortune are two buckets in a well. (German).
Fortune and misfortune dwell in the same courtyard. (Russian).

Some emphasize accepting misfortunes, as good will also come:

You win some, you lose some.

What you lose on the swings you gain on the roundabouts.

While this doesn't specifically advise calm, "you win some, you lose some" is a saying that emphasizes taking setbacks in stride and expecting both successes and failures over the long term.

Solution 4:

If I have understood the OP's request, they are looking for any expression or idiomatic phrase that suggests a person should avoid overreacting or feeling overly enthusiastic.

One proverb which advises people to be cautious even when they have received good news, is the following:

don't count your chickens before they're hatched (OLD)
Don't be too confident in anticipating success or good fortune before it is certain:

• ‘I wouldn't count your chickens—I've agreed to sign the contract but that's all I've agreed to’
• ‘We are feeling positive but not counting any chickens.’
• She wanted to buy a dress in case someone asked her to the dance, but I told her not to count her chickens before they hatched.

If the OP wishes to emphasize the aspect of being patient, then I suggest this very well-known proverb

Patience is a virtue (TFD)
It is good to be patient.

• Fred: The doctor has kept us waiting for half an hour! If he doesn't call us into his office pretty soon, I may do something violent. Ellen: Calm down, dear. Patience is a virtue.

Alternative expressions, which mean to look at something with objectivity and impartiality, are the following:

1. put (something) in(to) perspective (TFD)
   To clarify, appraise, or assess the true value, importance, or significance of something
   • Let's try to keep everything in perspective. If we put the matter into perspective, I think we can discuss it reasonably.

or...

2. sense of proportion (OLD)
   The ability to judge the relative importance or seriousness of things:
   • ‘Day-to-day life can grind away a sense of proportion and a sense of what is really important.’

_{OLD = Oxford Living Dictionaries
TFD = The Free Dictionary}