While the solution posted by Anthony will work, the question is how will that data be consumed? If it will eventually end up in some kind of report, then you may need to get this into a stored procedure, at which point making it work will require that the output of the query contain the exact same set of fields all the time. If both tables have exactly identical structures, you could also do it something like this:

DECLARE @AGE AS int = 59;

DECLARE @TODAY AS date = GETDATE();

SELECT *

FROM TABLEA

WHERE SomeDateField BETWEEN '1900-01-01' AND DATEADD(day, 0 - @AGE, @TODAY)

AND @AGE > 60

UNION ALL

SELECT *

FROM TABLEB

WHERE SomeDateField BETWEEN DATEADD(day, 0 - @AGE, @TODAY) AND @TODAY

AND @AGE <= 60;

If the two tables don't have the exact same set of fields, then you'll need to change the "*" to a specific list of fields for each SELECT, and use aliases when the same field from both tables has a different name in each one.