The AW139 was flying southbound toward Mangalore at 3,100 feet above mean sea level. At the same time, the PA-44 was conducting a practice instrument approach to Mangalore. The PA-44 commenced a missed approach from below 3,000 feet in a northerly direction toward Mangalore and the pilot broadcast that the aircraft would climb to 3,900 feet. Shortly after the PA-44 began climbing, the pilot of the AW139 received a traffic collision and avoidance (TCAS) alert and manoeuvred the aircraft to increase separation between the two aircraft. Both flights continued without further incident.