The most extended technique I know is the estimation of SR Ca2+ by applying a Caffeine pulse.... this triggers massive RyR2 opening and a Ca2+ transient you can measure in Fura-2 (some people do this with fluo-4) loaded myocytes.
If there is an alternative technique to really measure [Ca2+]SR I will follow other answers
Other alternative you can use to aproximate is to load the cells with Mag-Fluo 4 or other indicator that allow to monitor intraSR Ca2+, then start a protocol in which you can stimulate or not the cells during some time and apply Tetracaine (RyR blocker, to complete the store) and finally Caffeine to deplete the store.
We use to measure the SR [Ca2+] in adult cardiomyocytes loaded with Fura 2AM and with the application of 10mM caffeine as has indicated Luis. Fura 2AM is a fluorescent indicator that leads, by the application of a formula, to quantify the intracellular [Ca2+]. Other fluorescent indicators only can measure the changes in intracellular [Ca2+] but don´t quantify it