Depending on the scale, coordinating research can often be one and the same with project management. Both rely heavily on planning strategies and monitoring progresses. Each also has a role in monitoring budgets. In my experience, research coordination often is not involved in setting the budget, but rather ensuring the planned budget is well managed.
When coordinating research it is vital that decisions flow through you. In essence, you should be the funnel in which all decisions are channeled whether you are slated with making the final decisions or not. Often the team looks to the coordinator for reference and validation.
Equally important is knowing how to say you don't know. Some questions arise and you will not have the answer on the spot and it is important not to be shaken by that fact. In my experience, teams can appreciate it even more if you say "I'm not sure" and flow-up with an answer later.
The ability to teach others can increase productivity and provide avenues for team advancement. Providing opportunities for the team to advance their skills garners respect and gratitude.
Clearly written procedures and communications help alleviate potential misinterpretations. However, being concise and bringing attention to key points is also an impactful way to communicate with your team. My written communications are always thoroughly calculated to cover the tendencies of my team and are always a reference point for procedural conversations.
I believe it is important to be more flexible in talking with team members. Whether it is a presentation or a causal project conversation, it is important not to change policies without written evidence.
Intrinsic motivation can be a great thing, but some individuals need more extrinsic motivation. I always get to know my team to find the right way to motivate each person. Knowing your "why" is important, but when you understand the individual "why" of each team member then you will exponentially increase changes of success.
When dealing with teams there can be friction. Understanding how to negotiate with them can help everyone feel more understood and accepted. Challenges in life arise and can make something that was once simple very difficult. Trying to understand their challenges can help you shift tasks around more appropriately between other team members to help reduce burdens during challenging times.
Even when coordinating steadfast processes it is important to re-evaluate those steps to determine if there is room to increase efficiency. New products, more experiences, and technological advancements can all have tremendous impacts on current processes. I believe if you are not actively looking to improve then the chances that your procedures will be become obsolete will be continually increasing.