zastajati

1. to stop for a moment; to pause
   Šetali smo polako i često zastajali ispred izloga. — We walked slowly and kept stopping in front of shop windows.
   Govorio je tiho, zastajući posle svake rečenice. — He spoke quietly, pausing after every sentence.
2. (of breath, heart) to stop; to catch
   Svaki put kad ga vidim, srce mi zastaje. — Every time I see him, my heart stops.

The perfective is zastati; for halting speech, zastajkivati is also common.