Small Transport; Low Wing; 2 Turbojet Eng
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 4.5
Situational Awareness; Distraction
ATC Issue All Types; Conflict NMAC
Flight Crew Took Evasive Action
Aircraft; Human Factors
I was on the D-side position coordinating an inbound on Aircraft X who was on a vector for the visual approach.  When I came off the line the pilot told the R-side that he had a near miss.  When I looked I saw a VFR target behind the aircraft at 2;800 feet.  I did not see that aircraft before I went on the line to coordinate.  I also don't know if the aircraft had T-CAS because he never said anything about a TA or RA.I would recommend that Controllers are better trained to balance workload and service.  In a terminal environment there are times when VFR flight following is not possible due to the amount of traffic calls that are required.  It takes time and attention out of your scan for IFR traffic.  I would also recommend that Sector 03 and 04 be split earlier regardless of arbitrary traffic numbers.  Sector 03 is a unique sector and requires constant attention to traffic calls; if we split it all the time it is easier to stay on top of those calls.
ZMA Controller reports of an NMAC report he heard about; while off-line doing other coordination. IFR and VFR aircraft.