Of course sending a polite, well expressed, concise mail (tips 1, 2, 5, 9, 10 below) is only the start. Will they respond? We of course don't expect an immediate response (tip 12) but we do need an answer.
A popular option is to have no tracking mechanism and hope. This sadly (not everybody is as professional as you) can leave you exposed. Another route taken by many is to cc a request mail back to self. This has two disadvantages: firstly it is clogging the in-box and secondly it is allowing your in-box to be your driver. Instead, note when to follow up that mail on your master list. The latter is your flight-deck: your definitive list of what you have to do, want to do work and home.
It is a favourite pastime of seniors leaders in organisations to exhort their teams to do more 'joined-up thinking'. Those leaders sometimes fail to notice they have not unveiled the dots. Nor allowed a modest budget for pencil and paper.