You have two chances to catch Mesprit. If you accidentally make it faint both times, you can't catch it anymore. If you made Mesprit faint once, find it, trap it, lower its hp to 1 using false swipe (you should have gotten the TM), let it escape, then encounter it again and use a quick ball.
After you beat the elite four and the galactic biulding
A Master Ball
You catch Mesprit in HeartGold in Route 48 on either Mondays and/or Wednesdays while listening to DJ Ben's Marching Band. Or at least I think! Hope I helped^_^ ~ Kaede Nagase.
if you mean the map marker you can catch mesprit Pokemon of emotions with it hope this helps
Mesprit roams Sinnoh.
Catch better Pokemon
you can catch mesprit after the championship on the wild >
You need the marking map you used to catch mesprit You need the marking map you used to catch mesprit
the way you catch azelf mesprit and uxie.
chase it down
No, you cannot catch Mesprit in either of those games. To get Mesprit you can:Trade over the GTSTrade from Diamond, Pearl, or Platnium
If you have the marking map it will track mesprit, just don't fly.