Solution 1:

Here is some code, that converts NSExceptions to Swift 2 errors.

Now you can use

do {
    try ObjC.catchException {

       /* calls that might throw an NSException */
    }
}
catch {
    print("An error ocurred: \(error)")
}

ObjC.h:

#import <Foundation/Foundation.h>

@interface ObjC : NSObject

+ (BOOL)catchException:(void(^)(void))tryBlock error:(__autoreleasing NSError **)error;

@end

ObjC.m

#import "ObjC.h"

@implementation ObjC 

+ (BOOL)catchException:(void(^)(void))tryBlock error:(__autoreleasing NSError **)error {
    @try {
        tryBlock();
        return YES;
    }
    @catch (NSException *exception) {
        *error = [[NSError alloc] initWithDomain:exception.name code:0 userInfo:exception.userInfo];
        return NO;
    }
}

@end

Don't forget to add this to your "*-Bridging-Header.h":

#import "ObjC.h"

Solution 2:

What I suggest is to make an C function that will catch the exception and return a NSError instead. And then, use this function.

The function could look like this:

NSError *tryCatch(void(^tryBlock)(), NSError *(^convertNSException)(NSException *))
{
    NSError *error = nil;
    @try {
        tryBlock();
    }
    @catch (NSException *exception) {
        error = convertNSException(exception);
    }
    @finally {
        return error;
    }
}

And with a little bridging help, you'll just have to call:

if let error = tryCatch(task.launch, myConvertFunction) {
    print("An exception happened!", error.localizedDescription)
    // Do stuff
}
// Continue task

Note: I didn't really test it, I couldn't find a quick and easy way to have Objective-C and Swift in a Playground.